If you can, the disposables are the way to go. But, we couldn't when we went to Disney because Em does Pulmozyme and was in the ISIS study at that time. We had a Family Suite with a microwave, so we just boiled them there like we do at home. We shipped enough distilled water along with some other stuff to the resort before we left home, and packed our usual bowl that we boil in. It worked out great, and Disney was great about getting our package to us as soon as we arrived.
One more thing I always mention about Disney. If you're staying on the grounds, they were great about getting us a brand new shower head so I didn't have to worry about what might be growing in the one that was already in the room. They also gave us a set of Brand new linens every night for Emily's bed because she is sensitive to the smell of laundy detergents. They were fantastic about these things.
Enjoy your trip!