You'll be able to buy small bottles of soy milk (white or chocolate) in the food courts at the resorts and at some locations in the parks. Of the pizza CS restaurants, the only one I can think of off-hand that offers soy cheese is Pizzafari in Animal Kingdom. TS restaurants will have what you need for your son, but you most definitely need to sure to indicate his allergy on your ADR. At several restaurants, even though I had indicated that I don't eat dairy, I was able to have a meal made that met my dietary restrictions but they didn't have soy milk for my after-dinner or breakfast coffee even though my ADR was noted.
Also, you'll find some dairy-free treats for him like Tofutti and Rice Dream, as well as Divvies cookies and candy. The Divvies are offered in a few places around the hotels and parks; the non-dairy ice cream at the Plaza Ice Cream Shop (MK) and Beaches and Cream (Beach Club Resort). There's also a new bakery in DTD that has vegan baked goods (donuts, muffins, and more) so no dairy in them either.
Around two weeks before your trip, contact
[email protected] to review your son's allergy and where you will be dining. I'm sure they'll be able to give you more tips at that time.
I'm going to move this thread over to our "Guests with Special Needs" forum where others with similar concerns can pipe in, offer advice and relate their experiences.