The rides that are more rough are marked on the park maps with a red triangle icon to warn that there are some health warnings associated with that ride/attraction. There are also signs before you get into line and before boarding. But, it's up to you to decide whether the ride is appropriate or not. They used to have something on their official website about riding with a leg cast, but it was mostly info about rides where a leg cast would fit, rather than things they were recommending you not go on. They didn't have anything about arm casts and even the leg cast info is gone from their website now.
For some rides, like Dinosaur, Body Wars and Star Tours, the arm in the cast will be dead weight and might fly around. For others, you might find that you want 2 arms to hang on. So, find out what you can about the rides before you go; if in doubt, have some members of your party ride to decide whether the person with the cast should go; ask CMs about their ride.
And.....have fun.