I would take a disk only. I have the game but it's not readable by either wii or gc. I bought my son a GC because the wii has been having issues playing all gamecube games. Then turns out this game just doesn't work.
I tested the copy I had of WW on my Wii (I don't have a GC) and it played fine. Was yours the Player's Choice version? It might have just not read because it's scratched up; have you tried cleaning/buffing it?