Musical instrument can be played one handed I have limited use of my right hand and have always wanted to learn to play something
Percussion is great, the dtummer in a band lost one hand but the band didnt want to lose him so they created a special kit for him. Percussion just requires you to hit things, so it depends what you mean by 'limited use'. If you can hold a beater then you will be fine =) I play percussion and it is really fun! Im a drummer
you could also play the trumpet, it only requires one hand to press the valves down the other just helps you hold it up. We had a kid in my band who didnt have a hand at all and he played the trumpet. He said it took some getting used to but its very do-able.
you can always just do piano or keyboard with just your left hand, the opening to moonlight sonata was played with one hand, sounds fantatsic. or do what I did, not because of limited hand use but because I grew bored of bass for a while, train your voice :)