which controller is better to use for wave race 64? The original or the Hori Mini?

I was using the nintendo switch controller. But if you're talking 64 I always thought the original was fine.

To my knowledge, mostly the top runners use the original controller with a loose stick.

WR64 really needs an OEM stick - others are usable but never ideal. Drake Lake 1'10" was set with a really old, "sloppy" stick - this can help to kind of maximize the ability to hit the small +/- X values in the joystick range for those very tiny, precise adjustments