Smash Bros. isn't complete without a GameCube controller in your hand, but don't fret - Nintendo's got you covered, and support for the devices is coming to the Switch.
You'll be able to use the existing GameCube controller converter released for the Wii U, which makes sense given that it runs off USB.
Of course, it'll also take up both your USB ports on your Switch dock, so keep that in mind if you want to play with the classic controller.
So if you've already got the hardware, you're good to go! All you'll need is a copy of Super Smash Bros Ultimate, which launches December 7th on the Switch.