Take this with a grain of salt, but "related to Nintendo, but not directly" sounds an awful lot like Phoenix doesn't it?
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I was thinking about characters that fit this description. I'm kinda taking this to mean "character that's almost seen as a Nintendo character or strongly tied to Nintendo".
Phoenix Wright (I've always thought he feels like a Nintendo character, as much as possible without actually being one anyway)
Professor Layton (similar to Phoenix)
Crono (He first appeared on the Snes right?, I think a lot of people tie him to Nintendo)
Cooking Mama (she fits the bill, personally I can't see it but who knows?)
Travis Touchdown (I think his games have been exclusive to Nintendo consoles, I'm not 100% sure)
Some I'm not sure about:
Arle Nadja (like someone mentioned I've always thought puyo puyo was always multiplatform)
Monster Hunter (I know Monster Hunter is a big deal in Japan, but I don't know whether it's seen as a franchise with strong ties to Nintendo?)
Oddball pick:
The Denpa Men (I actually thought this was a Nintendo franchise, but I assume it isn't since these games have no presence in Smash whatsoever)
Not that I expect The Denpa Men, but can you imagine if Sakurai did include a character like that?