We attended last year's party, and they had one type of cookie available that covered several types of allergies. I believe it was the French Medow Bakery Chocolate Chip Cookie. We avoid peanuts and tree nuts, but this one was also gluten free and dairy free at least, and perhaps safe of other allergens, too, that I don't recall. I don't have allergies, but I tried it and was amazed at how good it was for being so "free" of allergens.
We found these at the Tomorrowland Terrace Noodle Station, which was one of the regular "cocoa and cookie" spots on the map. I had contacted special diets, but I don't remember what they told me. We did not have to make any requests ahead of time, we just walked up to the counter and asked for the allergy-safe cookie. They also had apple juice boxes instead of cocoa - maybe other drinks, too, but I'm not certain.
Hope you enjoy the party - we thought it was great!