Other ways to prevent blisters:
Wear shoes that fit you well and that you are used to walking long distances in. This may require you to test out some of your shoes and take a lot of test walks to get the shoes well broken in and your feet well adjusted to the shoes. But, the extra walks are good training for getting in shape for Disney (am I the only one who designs my workouts to be Disney specific starting a few months before the trip? Lots of longer walks, many with backpacks. More focus on endurance than on speed.). Also, wearing the shoes regularly before you go to Disney will help build up the needed callouses on your feet so that you won't have to worry about blisters (think of the callouses as your own, built in, mole skin.)
Mutlple pairs of socks will help some, especially if you start with a sock liner, microfiber, polypro, wicking nylon, coolmax, etc sock. That will help keep your feet dry to start with, but it alone (along with the anti-perspirant trick) won't completely eliminate the possibility of blisters.
Duct tape is also an amazing thing that can help prevent blisters. When you start to get a hot spot or blister, put mole skin (or just duct tape, works well too) on the hot spot and also on the shoe where it is rubbing on your foot. That should help smooth out the area and should go a long way towards preventing blisters. You can create a small roll of duct tape just by wrapping some tape around it self into a little roll, or put some on your water bottle so you don't have to take the whole roll with you.
Another alternative to mole skin is the Band-Aid brand (or 3M, but I like the Band-Aid brand. Don't bother with the store brands, they're not near as good) sport of foam band-aids. Get the large ones (2in wide) and cut the pad off so you have two pieces of slightly squishy, very adhesive magical foot relief. Works great and much less cost than mole skin.