I don't know the medication in question but I would call ahead to ensure that a standard microwave is available. I don't think that I would heat something like medicine in a food court microwave - they tend to be higher power than our standard home microwaves.
If Disney flat out can't accommodate you I think I would arrange a Wal-Mart stop and just purchase an inexpensive dorm type microwave before I would take a chance on unknown wattage in a microwave.
Hope you have a good trip! Travelling with cancer can have some challenges depending on the medication he is on but it is so worth it to spend the time doing something fun with family!