I've never heard of that version of the game causing problems, so it may be a later form of the laser with better reading capability. A scratch on a disc will almost never affect a disc drive the same way as another. A silver Gamecube is a later model, if I'm correct. And, after all, the Wii had more than 6 types of drives during its lifespan, so they could have changed out the drive in a later version.
However, I'd try cleaning the disc before swapping the drive.