Talk to your doctor and tell them that you want a wheelchair due to your trip. Some insurance companies will pay a portion of the rental fee if your doctor has written orders for it. Of course with your check in so near, it may be hard to find a smaller chair in your area, but I would start with a local children's hospital and see if they have a medical supply center ( ours does, but I may be spoiled by living near Birmingham). The worse case, you will have to rent a smaller adult size. It will be a little big for him, but it will be better than him having to use crutches.
I would also recommenced that if you are not able to find one prior to travel, then rent off site. You will find much better prices and much better product then renting in the parks. Another benefit of renting off site is that you will have the chair with you at your resort and any other place you go.
Travel with a wheelchair is not a " blessing" as I'm sure you have already figured out, but I think that Disney is one of the most accessible places we have been.