Theresa, I would look at the list in the FAQs. I think Cheshire Figment posted the link in this thread, and it's also at the top of the board. I personally have used Walker numerous times for
ECVs. I don't know the wc prices, but I recall seeing them in the past and thinking that they seemed very reasonable. A lot of people also like Randy's, but the feedback here for rental companies is largely for ECVs. I don't know if Randy's will require you to be there in person to get a rental wc as they do with EVCs, but Walker's just has your item waiting for you.
When you make your reservations, note that you would like a room close to the elevator due to mobility issues. That way, you will not end up at the end of a huge hall if you want to try to make it down yourself to sit, get coffee, or the like. Both have been very good about this, and we did not notice any noise being by the elevators.
For the Dolphin, you need to keep your wc/
ECV in your room. The Swan has a room off the lobby where you can leave your charger and stash your ECV/wc overnight if you prefer and I always take advantage of that for the ECV. Not so much of an issue for a wc, though. I suggest bringing a towel for the wc, as it is more comfortable and allows you and others to readily identify/distinguish your wc if you leave it to transfer to an attraction (although it will also have your name on it).
Have a great trip!

Cupcake