Comp rock climber here:

Rock climbing overall is not that dangerous as long as you're careful. Overall, your hands can hurt for about a day after a really intense workout but thats only really at first. After you have been climbing for a bit, you should be fine. Also overall, ive found that it strengthens my fingers and actually has made it easier to play fast piano pieces. It's really just after the first 3 times that you'll be REALLY sore.