Since Gecko OS seems to not work with BannerBomb, is there any other way to use cheat codes?
I have just been wanting to mess around with the cheats for a couple of my games, Zelda: TP for one, and Super Mario Galaxy.

No

Haven't tested it, but trying with Ocarina might be worth a shot.
I'm aware that Ocarina is part of Gecko OS these days, but whatever is causing Gecko OS to crash with Bannerbomb, may not be present in a version of Ocarina.
http://wiibrew.org/w/index.php?title=Ocarina&oldid=28791