My daughter uses a wheelchair. Once, when we were staying at the Poly, her chair got a flat tire. To make a long story short, I went to guest services and asked if they had a childs wheelchair I could use. I noticed an adult w.c. behind her. She checked, and said she was sorry, they didn't, but if I could wait a few minutes she would get me one. I took the disabled w.c. back to our room, and by the time I got back to guest services, there was the child's w.c. We used it for the length of our stay.
One thing you may want to consider, does your son need to keep his foot elevated? I don't recall if the w.c. at disney have elevated foot rests or leg pads. You may want to call first to make sure. If you are staying on site, the w.c.'s are complementary, but there is a deposit that must be put down. It's refundable, of course.