Be aware that the parks have very limited supplies, and could run out at any moment. If you will absolutely need a wheelchair, your best bet is to rent one ahead of time, for the duration of your stay.
Do you have someone pretty sturdy and in good shape to push a wheelchair? There is a knack to it that takes some time to catch on to. Pushing someone in a chair, especially a large person, gets very tiring, too.
If your grandmother can handle a scooter, I'd recommend renting one of those instead. She will feel much more independent, and no one else will get worn out pushing a wheelchair.
"Too many people grow up. That's the real trouble with the world, too many people grow up."--Walt Disney
With the Disney wheelchairs, they can be only used between the two parks. Disney wheelchairs cannot be taken into downtown Disney. if you need a chair to get from the transportation or a hotel, I would rent from an outside source.