hello we had several members come in with similar capabilites and like for them i recommend for you - games playable with one hand:
wii sports resort
wii play (upcoming sequel)
dragon quest swords
virtual console and wiiware games (notably final fantasy 1 and defend your castle)
the wii is better suited to you than you might think. you can save the classic controller for your friends and search the wii titles more suited to you.