Rachel, would you be able to do grip work with that hand, even if it's just taking a tennis ball between the tips of the fingers and squeezing it? Also, if you have ever watched the videos of Kyle Maynard on the Crossfit website, I wonder if it would be possible to do pulls on a ring the way he does--slip you arms through the rings themselves up to the elbow, balance them at a point on your upper arms, then pull yourself up by pulling your arms down. It's difficult to describe, I will edit this post with a link to the video if I can find it.
a picture of the movement I'm thinking of. It would probably scrape your arms up a bit, though--maybe you could do it in a long-sleeved shirt.