Hmm, this is very interesting to me. Our experience was completely different, so I thought I would share (apologies to the OP--this is off topic)
My DS's hemangioma appeared on his left temple when he was one week old. It did bleed occasionally, but at age 2 months when it was about quarter sized and beginning to be raised, we consulted with a plastic surgeon.
Even though he and our pedi felt it would involute on its own, the concern was that it was near the eye and growth could cause distortion of the skin surrounding the eye. That would require plastic surgery later to correct.
So, we started laser treatment (no nerve endings--no pain) and cortisone. It was completely gone after 5 laser treatments every 4-6 weeks.
Just wanted to mention another noninvasive option to those of you faced with this. The laser treatment is most effective when started early, and we would have done nothing if the hemangioma were not on his face.
And to mikesluss---the CM's and characters are used to seeing all sorts of disabilities imagineable, and I believe they would never call attention to something like that. Don't worry--in that respect I believe Disney is a class-act!
To the OP, definitely discuss with your pediatrician what to do. He may provide you with butterflies, etc, and I would be sure to carry a small clean towel in a sealed bag in case you needed to apply compression. And I would certainly call an ambulance before I would drive.
Enjoy your trip!