If you have to try a stage a second time, be it from failing and going to the map screen, or you only got a flag and are going for a crown, you can select which set of characters to use. Zamus/Pikachu is available IIRC. If not, and only Samus/Pikachu is, try using the c-stick. During the Great Maze, where you can select any character, c-stick over to flip Sam to Zam, and Zelda to Sheik. Other than that up down up is your only option.
How I do it: Put your first and middle fingers on the up/down taunts respectively. They will not be leaving this position or sliding in any way. I turn the controller sideways so move your hand (or arm?) left and right really quickly. It feels like you're just movign it left/right but it works. I don't know how else to explain it, but don't slide your fingers all over and tear the skin off.