My friend’s dad went to Disney with a cast on his arm. It was cool because he brought a Sharpie so the characters could sign. However, it was not waterproof, and the rain caught us off-guard one day. My mother ran into a gift shop asking for a bag, and they were reluctant to give her one, but when he came in wearing the cast, they understood.
He was able to ride all of the water rides with a shopping bag tied over his arm, though. Now they have that new waterproof cast technology (this was back in 01), so that’s probably not even a problem, anymore. But the rides weren’t a problem at all - not even RnRC with the over-shoulder constraint.