I Might Sort Templates By Things

[Kappa]

Jokers by Lockpicking Skill:

Listed in increasing order. Nonmagical skill only, for the most part. Close ties broken by how often/frequently they've used it. Omitted Jokers either haven't picked any locks, or I'm not sure where they fall in the ranking. Note that even the very top of the list isn't bad at it.

Harley, Andrea
Felicity
Winter
Trick
Furnace
Loel
Celosia
Victor
Feral
Jun
Trouble
Micaiah
Mercy
Kas
Jellybean
Joker
Cindy
Queenie
Ghosty
Surprise
Rolan
Lalita

[anthusiasm]

Ok, wow, that is an impressively detailed trauma scale.
So what is it about the number clusters that would rule out the possibility of a Nolanverse Joker? And could the unclustered/special Jokers become Nolanverse Jokers?
Also, could you sort Sherlocks in order of current levels of self-hatred? How about Tonies in order of most-likely-to-respond-well-to-being-hugged by random strangers? (If there's any differentiation there).

[Kappa]

The 0 and 1 clusters couldn't produce Nolanverse Jokers because they rely on explicitly fantastical or sci-fi elements that contradict the "gritty realism" premise of the Nolanverse. Since unclustered Jokers aren't... clustered, it's hard to say if they "could become" Nolanverse Jokers - I mean, in order to port Joy to the Nolanverse you would need to make him not a dragon and not living in Equestria, at which point it's highly debatable whether or not he would still count as Joy. It's theoretically possible for there to be a Nolanverse Joker who doesn't belong to an existing cluster - but when I come up with a new backstory configuration that seems Nolanverse-compatible to me, I tend to just call it a new lettered cluster. Rolan is the current example of this. There isn't a Nolanverse Joker of him, but since there could be, he's listed as D-cluster instead of unclustered.

If you mean "could an unclustered or special Joker move to a Nolanverse and become a The Joker there?", the answer is... maybe, but I'm highly unlikely to write it.

Tonies by Hug Openness, increasing order:

Do Not Want
Iron Man [Edda]
Iron Man [Yggdrasil]
Hyperion [Cape]
Screwdriver [Atlantis]

Some Misgivings
Tianthonet [Thilanushinyel]
Fusion [Apollo]
Sapphire [Helios]
Red [Sunshine]
[Opportunity]

Sure Why Not
[Arceus]
Niva [Circle]
Ninette [Hogwarts]
Rocketship [Fantasia]
Tia [Quinn]
Iron [Chronicle]
Brightblaze [Equestria]

The "Sure Why Not" category has the smallest intracategory variation of all of them. The two Iron Mans are virtually indistinguishable. Screwdriver actually will hug random strangers, you just need to ask first or he may become upset.

[Kappa]

Sherlocks by Self-Hatred:

Listed in increasing order. Ties broken by general unhappiness level. Some Sherlocks not listed if they haven't been threaded and I don't have a good handle on their emotional state.

[Phaeton]
Minus [Sunshine]
[Nexus]
Strat [Downside]
Silver Streak [Equestria]
Sage [Avalon]
Sherial [Thilanushinyel]
Sary [Quinn]
[Arceus]
Steel [Chronicle]
Severine [Hogwarts]
Plus [Apollo]
Cloud [Helios]
Rahi [Circle]
Pearl [Atlantis]
[Fantasia]

[Tamien]

Jokers by SCP Object Class (Safe, Euclid, Keter). I predict most Jokers are class Euclid, because they tend to be powerful and hard to predict/contain but not actively inimical to humanity.

[Lambda]

There's pretty much no way an anomalous sapient is Safe. Brilliance might be Keter, and possibly any mint Joker.

Note that Jokers are much more likely to be destructive/hostile once the Foundation starts trying to contain them. Jokers don't like being contained.

[Tamien]

I feel like it's theoretically possible for an anomalous sapient to be Safe, but it would require some Damn Good containment procedures, and if anything anomalous were going to be Safe, it wouldn't be a Joker, precisely because of Joker resistance to containment and general unpredictability. Stella has literally in-canon devised containment procedures for rogue mints, but I doubt that's enough to render them Safe. Non-anomalous Jokers probably count as Safe, though?

I suspect that anomalous Jokers that SCP gets its hands on would become Keter even if they were originally Euclid, for the reasons you mention. Brilliance is definitely Keter-class in terms of destructive power and SCP might consider him volatile enough to classify him that way. Also I've been poking around, and apparently "Thaumiel" is a class now? From what I've read about it, I wouldn't rule it out as a possible Joker classification either. It's basically "this thing is a Keter-level object which is or can be used to counteract Keter-class anomalies" - an anti-Keter. I'm not wholly convinced on it as a classification yet, but if anything could be Thaumiel-class, a Joker could be.

[Kappa]

Brilliance would not be classified Keter for very long, because the Foundation doesn't have the resources to actually contain him unless they have some tame SCP that can do it, and I can't think of any off the top of my head and need to not read any more SCP entries in the next little while because it's becoming a damaging obsession. So either he'd dimension-hop and they'd never see him again, or they'd chase him down and escalate containment procedures and he'd crack the planet in half. I mean, I guess in the first case they'd still have records of him afterward.

Frankly, I wouldn't class even the most mundane Jokers as Safe. Particularly not if you factor in dreaming to Milliways and potential freecasting.

I'm giving most Jokers a base rating of Euclid, and assigning Keter to the ones who stand at the intersection of "obvious potentially destructive powers" and "reacts very badly to attempts at containment". The Keter list is therefore as follows, in increasing order of how freaked out I imagine the SCP folks would be about them:

Euclid under consideration for Keter
Ghosty - Completely impossible to contain; all they can do is hope she never decides to do anything horrible with her mysterious and unsettling matter manipulation powers. On the other hand, she's not doing anything horrible with her mysterious and unsettling matter manipulation powers.
Mercy - His powers don't have the kind of scale necessary to be worrying in their own right, he's unlikely to express worrying levels of hostility, and he doesn't show any sign of being especially durable in comparison to ordinary humans, but he'd find captivity upsetting and his magic is sufficiently versatile to make him hard to contain.
Corona - He probably wouldn't be emotionally together enough to make serious escape attempts, but I can imagine his Gift would be pretty terrifying to anyone with half a clue about the variety of possible applications - on the flip side, I bet they use him to try to duplicate things a lot...
Winter - He'd be sufficiently resigned to captivity sufficiently fast that there wouldn't be any major worry about him getting out, and not that huge a worry about him killing anybody, but he's strictly impossible to kill, emotionally volatile, and probably makes God nervous. Maybe they'd put him in a room with 682 and see if one of them managed to take out the other one.

Keter
Aianon/Ansharil - They wouldn't try very hard to get out, but they are scary and any hints about their powers would probably be very upsetting. I can imagine the SCP people treating Aianon like another 682, if a rather less hostile one.
Sigyn [Edda] - He's an Asgardian. It wouldn't take that much to keep him nailed down, at least not in comparison to the people farther down this list, but he would be very, very unhappy about it and probably issue enough nasty threats to give the impression that he's just waiting to go on violent rampages the minute he gets loose.
Victor [Avalon] - He has overactive regeneration powers to the point where he's hard-bordering-impossible to kill, and he's an obligate carnivore with no taboo about eating humans. Again, shades of 682, just in a smaller and slightly more manageable package. Getting less and less manageable as they continue trying to manage him.
Morrigan [Hogwarts] - He is going to have a magical incontinence problem similar to Feral's, but where Feral tends to emit fire, Morrigan tends to emit sharp. And he would be deeply unhappy about captivity.
Loel - He's not actually that likely to freak out hugely, but his powers are sufficiently gruesome and he's sufficiently creative with their potential applications that there's a good chance of an escalation spiral - they try to contain and study him, they keep upping the severity of the containment procedures when they find out about the shit he can do, he keeps getting more upset about the containment procedures, they try harder to contain him because nobody wants a highly agitated blood-controlling anomaly on the loose...
Feral - You bet your ass he'd freak out hugely. And even if you take away his wand, he can still set your ass on fire.
Furnace [Dragaera, unthreaded world] - Irrevocably bonded to a bladed weapon that can selectively destroy or capture the soul of anyone it cuts, and has other subtler powers the Foundation would have trouble fully understanding. Would not be especially shy about using it to escape captivity.
Brilliance - Has, and would explicitly threaten to use, the capacity to destroy the planet on which they attempt to hold him.

I didn't include any non-Effulgence Jokers, but special mention goes to Teah, who would end up Thaumiel because it is so blatantly impossible to contain his god-part that it wouldn't really come up as a problem, and by default he is very nice to everyone and very, very powerful. Probably SCP agents/etc. above a certain clearance level would be required to know about him so they could pray in emergencies and hope he's online at the time. If they found out about his mortal forms they'd probably have protocols in place to find, capture, and inform the new body of their godly status every time the old one dies.

[Lambda]

I think the Foundation would try to keep Teah's mortal part awake, specifically so as to prevent the candymagic from happening. Sure, it seems like a friendly helpful wishgranter, but who knows what its motives are, really?

On the other hand, they keep 458 in the breakroom, so who knows.

[Kappa]

I see what you mean, but I feel like Teah being Teah would ultimately win out there. Also, it's pretty hard to find Teah's mortal forms, and takes lucky guesswork to even know he has one unless he notices and says something. For sure, if he showed up anywhere that wasn't already under close Foundation surveillance, there would be at least a full night's sleep worth of prayers granted before they even had enough information to suspect the wish-god of being a dreaming human - and for sure he'd give priority to neutralizing dangerous SCPs and generally reducing the amount of horror going on in the world. I just don't see them looking at the aftermath of six hours of Teah and going, "It must be stopped," instead of "Where can I get five?"

Edit: And lo, Alicorn hath split the topic.