Do I Have to Use the Classic Controller with Virtual Console Games in Wii Mode?
Wii U
Important: Although there is a GameCube Controller Adapter available, it can only be used in compatible games (currently only Super Smash Bros. for Wii U). The Wii U console is not otherwise compatible with GameCube controllers.
Some games are playable with just the Wii Remote, while others require use of the Classic Controller attachment.
The best place to go for information on which controller is used for a specific game is the Wii Shop Channel catalog itself. Each game clearly shows which controller(s) it uses.