Hardware Hacker "Hasse" modified a GameCube controller for his disabled brother, so he could play GameCube games on his Wii one-handed. It's a really clever modification, with tilt-sensor and very helpful guide-lights.
There is an alternative solution out there for the lay-person, although it of course will cost more money. Connect one of a range of Playstation 2 one-handed controllers to the Wii/GameCube using an adapter. Simples.
And whilst on the subject, I highly recommend taking a look at Giant Bomb's cross platform list of compatible games for one-handed play.