I have the original connection cable for my SNES (The one that looks like a cable TV wire), and I was looking into getting the AV (Red/Yellow/White) connecter cables for the system. However, after looking on Amazon, I noticed that the cables are noted as working with the SNES, the N64, and the Gamecube. I then used my Gamecube's AV cables with the SNES, and the system seems to be working fine (It actually has better image quality now). Will continued use of these cables harm the system in any way?
Not at all. The system was designed to be able to use both types of cables.
As a word of advice though, you may want to check a local used video game store first if you're looking for the cable at a decent price. Or, since it doesn't seem logical to be playing the SNES and the GCN at the same time, you could always just plug and unplug the cable from one system as needed.