Isaac and Chibi-Robo are more so popularly seen from others, but have some uniqueness to them.
Sukapon doesn’t really have more than one game to himself, but he is from Nintendo’s first enjoyable fighting game, and already has a fairly distinct design and moveset, so I’d say let him in.
Dr. Wright…the Sim series is big, and while it is usually EA-associated, Dr. Wright is specifically a Nintendo-owned character, it seems, so he goes here. Having him create buildings, manage resources, send out natural disasters, or even another big Bowser to attack like a Kaiju…I think it’d be fun.
Someone from Smash…this can be Sandbag, Primid, Tabuu, Master Hand/Crazy Hand, or even the technicality of Dragon King.
Undo Dog…another weirdo, and a dog who’s abstract/cartoony enough, unlike the Nintendogs and like the Duck Hunt Dog. Mario Maker is a fairly liked/successful Mario spin-off, as was Mario Paint back in the day, and I’d like to see what kind of strangeness they could make with a moveset that has aspects of both.
Ganon…the pig with the trident, flame bats, various other magic attacks, etc. Unique weapon, unique Ganon moveset, but you can keep FalconDorf, if you really want.
Punch-Out…Punch-Out is such a fun, well-designed series, and the enemy boxers of the series are very distinctive. Aran Ryan has moveset with all his cheating shenanigans but isn’t the most iconic. King Hippo, Bald Bull, and Glass Joe probably the most iconic (original) boxers in the series but it’s variable how much moveset potential they have…though I think you could convincingly enough turn Bald Bull into a grappler, and especially have King Hippo attack with items associated with him (crown, manhole cover, pineapples)…they don’t have to as rigidly stick to boxing as Mac does. Doc Louis is a good non-enemy candidate, sticking around as long as Mac does, and he has added gimmicks like chocolate bars, his bicycle, maybe training equipment. I do know that this series isn’t as iconic in Japan as it is in the West, but still, it’s a wishlist.
Team Rocket/Team Grunt…basically, an evil team trainer from Pokémon who works completely different from our heroic(?) one. This Grunt, in fact, fights themselves, with various items from Pokémon games, even the card game or anime, perhaps. Sometimes Pokémon are also summoned to supplement. I either imagine that or Meowth with Jesse & James as a strange Wolverine/Doronjo hybrid. The only issue I see with this is that people would be disappointed it’s not just a regular Pokémon itself. Think three-dimensionally, though, yes.
Does Captain N fully count as “first party”? Probably not, given the rights are probably split with DiC, but he is entirely themed around Nintendo, comes from the other most famous Nintendo-themed crossover, and he could be another interesting “full circle” thing in a similar vein as the outright Smash-Brothers-based fighter. I imagine the Zapper is a given, and maybe any other NES controller/peripheral is fair game for a moveset, as well as what’s already in the show or comics (teleporting in multiple directions, enhancing his jumps, the “Pause” feature, and other random features the Power Pad had).