I shoot with my right hand, but do all my baton-twirling with the left. (Curiously, though, I use my right hand more when I'm doing rhythmic gymnastics.)
I play the mandolin with my left, but with timbrel and the Tyrolean harp, I do better with my right foot. Like most people, I tend to use my left nostril when playing Jew's harp.
Swordfighting I do mostly right-handed, but I find the Agrippa defense works better left-handed.