Like most everyone else here, I play most stuff better righty even though I'm a lefty. I will say I can't play a DS right-handed, though, and I've never had the Wiimote problem fortunately.
(Most likely because I always play righty when using the wiimote+nunchuck unless there's a lefty option)
Funnily, most other photos of Shigeru Miyamoto show him holding the Wiimote with his right hand and nunchuck in his left. I do the opposite, unless I'm forced to switch hands (Wii Sports Resooort!)
I don't know any left handers who haven't conformed to using everything normally other than writing with their left hand. That would suck having to use everthing the wrong way.