I'd be fine with Nintendo exploring a new genre with an existing IP. As long as it doesn't affect the release of the original.

Well, I'm not too sure about a Captain Falcon spin-off.. It could bomb even worse than Game and Wario, or it could even sell decently! We can't know for sure!

I wouldn't mind a GTA-inspired spin off to F-Zero for Wii U, with Captain Falcon as a bounty hunter in an action adventure game. The game could use the new Zelda U engine, but be set on various planets in the galaxy. Nintendo could combine the GTA inspired action adventure game for Wii U with the release of a true racing sequal to F-Zero for both Wii U and 3DS, using the Captain Falcon Amiibo to swap data between the three games. For instance you could play the action adventure game on Wii U using the Captain Falcon Amiibo, and through that game enter various racing areas where you transfer your Amiibo stats to the racing game to collect prize money from races that can later be used in the action adventure game.
It should also be possible to upgrade the galaxy with new planets and other areas through DLC making it a game world with infinite possibilities.

To my mind, a Captain Falcon game should look like a cross between Viewtiful Joe and the Arkham games.

One city to explore and your basically beating up thugs and collecting bounties, but in a comic book style. Thematically I'd like it to be dark, hunting down serial rapists, people traffickers etc, but presented in a bright, primary colour fashion. Not unlike Suda51's games.

The only issue is that I can't think how to introduce an element of three dimensionality to it. Half of the fun in the Arkham games is ignoring the streets and exploring the skyline, but without completely changing Captain Falcon I can't see how you'd accomplish that.

Captain Falcon Punch-Out!!

I also pictured the game like Sly cooper. The team aspect. There's a ton of characters they could let you also use. And be used for story material.

Pretty much figure that to be Wonder Red from The Wonderful 101.

Consider how similar Wonder Red and Captain Falcon really look like.

At one point TW101 was allegedly supposed to be a collection of Nintendo characters before the big N nixed that idea. Wouldn't be surprised if Captain Falco would have been the main character in such a version of TW101.