Short answer: There is no “Super Mario 64 Wii” edition. The game was developed for the Nintendo 64 and never received a ground-up Wii remake. However, you can play the original N64 version on a Wii—via the Wii Shop Channel’s Virtual Console service (discontinued in 2019).
Contrast with Super Mario 64 DS (a full remake with new characters, levels, and touch controls) or the Super Mario 3D All-Stars version on Switch (upscaled, widescreen, modernized controls). The Wii Virtual Console release is a straight emulation—preservation, not reimagining.
The Wii Shop Channel closed in 2019, so you can no longer purchase it digitally. If you bought it before closure, it remains in your download history. Otherwise, your options are:
So while “Super Mario 64 Wii” doesn’t exist as a distinct product, the classic game is playable on Wii—just don’t expect a Wii-specific version.