A cast anywhere is not a lot of fun. Plus, you have to worry about getting it wet, so washing hands, showering, etc, all gets more complicate. Do you have an expectation that one could alleviate your pain considerably, based on medical advice? I’d get all the information possible on this before opting for a cast over a brace. Perhaps using a sling during park days would provide some additional (and removabe!!!) support, and act as a reminder to not use that hand/wrist unnecessarily. Tightening a sling could also help prevent jarring or arm flailing where you can’t grip with both hands.
honestly, the thrill rides would be my least consideration, as most are not as intense as you might expect. Big Thunder is bumpy but bracing your feet and holding on with one hand is easy enough. If your pain level is likely to remain high two weeks following this injury, the best advice is to reschedule, if possible.