Good news for those who didn't pick up a GameCube controller adapter for Wii U. Nintendo has confirmed that they'll be releasing a round of new adapters for Switch. These will let you use your GameCube controllers on Switch, and will cost $20. If you do happen to have the Wii U adapter, you'll be good-to-go with that one on Switch.
Furthermore, Nintendo is going to release another round of Smash-branded GameCube controllers as well, but pricing on those controllers was not discussed.
Don't feel like buying an adapter or a GameCube controller? No worries, as Smash Bros. Ultimate will support the Joy-Con, as well as the Switch Pro Controller. You can even play with a single Joy-Con!