If you have a disabled placard for a car bring it.
Read the FAQs for this board as there are numerous links listed to things like wheelchair rentals, GACs, specific problems, and accessibility.
I am a waddlerump and have damaged knees and a disintegrating disc. I spend my time setting on my bed so I can constantly be shifting positions. I cannot stand for long periods of time as I get lower back pain and sciatica type pain. That said what is my point, lol.
WDW cannot ask for proof of disability. I would bring it as it won't hurt to have it even though you will not need proof. I have never been asked proof of my disabilities not even at the Wild Animal park where I got free admission for being mom's companion.
You do not have to stay in the wheelchair or ECV and if someone give you grief then politely tell them to stop assuming. I use an ECV but will at Wal-Mart get out to reach stuff or to get into type spots. At parks I get out and go into a store rather than be a china store heffer.
Using a wheelchair is easiest because of the ability to fold the chair and get around tight spots. On the train an ambulatory person can climb on the train while a friend puts the chair on the train. Some wheelchairs have leg rests which can be elevated and thus help a sore leg.
ECVs are nearly impossible to get comfty in. Powerchairs allow the user the freedom of a wheelchair but they do have to get out for certain rides that only take standard chairs.
ECVs are the mules that carry everything and are a good choice if a person can walk. I use only ECVs because I can stand in line for a while and even climb stairs but without one my day's end is 3 pm instead of midnight and I aint moving around the next day much. It is easier for a friend to talk to a person in an ECV than a wheelchair. I think this is your best bet. Use the ECV then when you come to a shop just hop out and have fun shopping.
The nurse's station which has ice packs and other remedies.