My DH and I stayed at YC over New Years Eve. You are right that everything is rather spread out. It's convenient to walk to MGM and Epcot, but anyone with health problems would not find it easy becasue it is quite a way and there are hills. The boats that you can take to both parks might be more than he can walk to also. And, if he has a wheelchair, you would be able to go to the BW area which is really nice.
I've seen some of the same posts that talk about the wheelchairs available at the resorts, some people are very pleased and others found that the available wheelchair was either in poor condition or didn't meet their needs (like an extra wide when they needed a narrow one, or vice versa).
Even if you are driving and bringing the oxygen with you, you will still need a back-up medical company in case of problems with the oxygen. All of the companies that Cheshire Figment listed (except for Randy's Mobility) are full service medical companies that also provide oxygen. Since you will need to be dealing with them anyway, you may as well rent a wheelchair from them too (and they will be able to provide one with holders for oxygen tanks, as Cheshire Figment mentioned).