I think I've found a character more obscure than Dunk and Shoot. "Whizz!" was an isometric platform game for the Amiga, DOS, SNES, and later the PlayStation. Brought to you by Flair Software, whose library of games includes.......absolutely nothing else of note. Sorry.

That's "Whizz" as in "Wizard" by the way. Because magic rabbit. The advertising made a bunch of urination puns, probably screwing any chance this bunny had. I actually like this game somewhat, it seems like something I would have made and it's from the 90's. There are speedruns of the game, so at least some people know the character, but you can imagine what trying to search the 'net for him is like.