There are adapters which allow a GameCube controller to be read as a Classic Controller. I'm sure it'd work with the new game.
Me, I'll probably just try and play with a Wii U Pro Controller. The GameCube pad has had a good run, and I'll continue to use it for the previous games, but I'd like to try something new.
Then again, I always get tripped up trying to play the older games with a Classic Controller. The A, B, and X/Y buttons are placed so beautifully on the GCN controller that it feels so natural.