I don't think Wolfenstein's impossible, just microscopic due to Doom already filling that niche and Halo being one of the most influential shooters.
Aside from the already mentioned. I'm going to start by posting a relevant video from FPS Youtuber Raycevick:
Both CoD and Battlefield suffer from severe fatigue at this point, and I don't think either has a bona-fide main character that acts as a central focus for multiple games. Really, it's a sideeffect of what Raycevick's talking about - the annual releases pretty much makes sure that not even a single player campaign's safe. As far as Destiny, don't know much, so I won't comment. Not counting on that at all though. Both these games also are too focused on the weapons to make for viable Smash reps.
I could have seen Mass Effect, if there weren't two interconnected problems: a) Nintendo would have to deal with EA for a ME rep, and you know how hated that would be, and b) Andromeda. The PR disaster around that hasn't settled, not with Anthem kind of repeating that.
Battle Arenas like PUBG, Fortnite and Apex are designed to be (almost) purely online with blank slate avatars. (Counter-Strike and similar games - although not battle arenas - are disqualified for similar reasons.) Works for the games themselves, but here's where my personal dislike for such a rep comes in: It would be really limited. Fortnite, for example has a building mechanic - but it's instant, with the player character holding a sketch and then boom stuff gets built. It allows for intense matches in game, since it's designed with guns in mind - but such a mechanic would threaten to break Smash and make the Fortnite rep OP beyond repair. There's very little that can be adapted into Smash, and that's my beef with it.
Really, the only others with a non-zero chance (whether they're merely included or can work as fighters) I can think off would be Overwatch / Paladins and Valve's Orange Box trio. Paladins has the luxury of a Nintendo Switch port, while Overwatch doesn't. Also, while I feel any Overwatch rep is extremely unlikely partly because A-B has other options (Crash foremost). Paladins has another positive: the only other High-Rez property with a Nintendo presence is SMITE (yeah, SMITE also got a Switch port. It might be only a matter of time until other MOBAs like LoL or Dota take the plunge and go on a Nintendo platform). However, Paladins (and SMITE) are not mega popular exactly.
Half Life has a massive advatange: Namely, 1 and 2 are seen as all-time classics, with 3 being a legendary meme. 2 especially introduced the HAVOK engine - and Gordon has a very unique gun in the Gravity Gun (which at least could theoretically work for grabs, if not more). Portal likewise introduced a non-standard gun. Both lack the Nintendo presence, though, which is a major downside. And Valve's shifted to an online focused model, so it would take a lot to signal that they're willing to give Gordon and Chell another chance. Heavy Weapons Guy is actually semi-popular here, not sure personally on if Valve's interested in giving TF2 a Switch port / a shot in the arm though.
Out of the FPSes, I honestly think that Doomguy's the safest pick, and Master Chief seems kinda likely if there's a second or third Pass. I could see an RE pick too. Outside of them. I'd be really interested in one of Valve's characters and an Overwatch / Paladins character. Technically Deus Ex's a shooter, but I'm not sure if it should be classified as that.