I have Parkinson's with balance, mobility, and stamina issues. I can't walk distances (use a cane for short distances like from a handicapped parking spot to a restaurant entrance). I can't stand for more than 5 minutes, and I tire very easily. But I still love going to Epcot and have an "Epcot After 4" annual pass. The other parks are OK, bit we love Epcot.
I use a mobility
scooter when we go to Epcot. I order it on-line from Scooter Vacations and have it delivered to the Swan Hotel. We valet park at the Swan, pick up the scooter keys from the Bell Captain's desk, and take the back entrance to Epcot. It's a nice "drive" from the Swan, through the Boardwalk area, to the park entrance. It's rarely crowded, and after entering the park, you're right around the United Kingdom and France pavilions in the World Showcase. Most everything we want to do and see is in the World Showcase, but we always go to Soarin' on the other side of the park. Before we get on the ride, we stop at Club Cool, get a free Coke, and go to a huge room that winds around behind Club Cool, where we relax while re-charging the battery of my scooter. There's also a Starbucks in the immediate vicinity if you want a little snack.
When we decide to call it a day (usually no more than 4 hours later), we go back to the Swan, park the scooter in the designated area, turn the key over to the Bell Captain, collect our car, and head home. Having the scooter delivered to the Swan means we don't have to disassemble and reassemble it and load it into the car, a real benefit.
If you're staying at one of the resorts, you can have a scooter delivered to your hotel, and you can take it on the busses, trains, and the monorail. Your traveler would still maintain some personal control over his mobility.
I hope this info helps and that you have a great time on your vacation.
Queen Colleen