Massive
Smash Champion
I don't think you being aware that you're using a wavebird would have any real effect on the time between when you hit a button and when the action appears on screen.If someone wants to set up a double blind where I can only see the TV and they can hand me a controller. I won't know if it's wired or not, and I am confident I can tell if it's a Wavebird or not up to 95% accuracy.
The easiest way I can imagine to conclusively test this is to film someone's hands (and simultaneously the screen) as they play with both a wavebird and a regular wired controller, hooked to the same controller port, playing the same character, on the same stage, etc. Film the movement of their hands and how long it takes for the actions to appear on screen for both the wavebird and the gamecube controller. A high-ish framerate camera (60fps ideally) would be preferred, but even NTSC standard (29.97 fps) would probably be enough easily to note any multiple frame difference.