OK, MK it is, then. I'm leaving out shows, since you said they won't work.
When you come into the park, he can stay in his wheelchair to ride on the train. The only loud part is when they blow the whistle (and the wheelchair car is right behind the engine). You may need to listen to the train for a while to decide if he would be aok with that. There is also a an announcer talking about the differnt areas as you go thru them. That's a bit loud too, but not too bad. You can either do a round trip on the train or get off in Frontierland or Mickey's Toontown Fair.
There are a lot of shops down Main Street, but no shows or rides.
In Tomorrowland, he could stay in the wheelchair for Buzz Lightyear. Your car can spin, but you are the one who spins it, so it can stay pretty stationary. There is a fairly constant noise level on the Buzz ride. He might enjoy watching the race cars in the Tomorrowland Indy Speedway. There are a few other things in Tomorrowland, but they don't meet your constraints about noise.
In Mickey's Toontown Fair, you can drive the wheelchair thru Mickey and Minnie's houses and go into the Hall of Fame for Character Greetings. Donald's boat is wheelchair accessible, but he might get wet, so I don't think you want to go in there.
In Fantasyland, he can stay in the wheelchair for Winnie the Pooh. I don't think he'd have a problems with that. There are some parts that are a little dark, but the noise level is fairly constant. He can also stay in the wheelchair for It's a Small World. My DD didn't like that ride when she was little, but she's OK with it now. The Small World song is playing constantly during the ride and there is a lot of movement going on all around you. I think it was just too much stimulation. She would stick her thumb in her mouth, with her arm over her eyes and her other arm over her ears. You might want to go on that ride without him first so you can decide if he'd like it. All the other Fantasyland rides involve getting out of the wheelchair.
At Liberty Square, you can ride the steam boat. It leaves every hour and half hour and is a nice, slow ride. The only noise would be when the boat whistle blows.
There isn't anything in Frontierland that meets your criteria, except maybe going to Tom Sawyer's Island. A wheelchair can go over on the raft, but not all the paths are wheelchair accessible.
There isn't anything in Adventureland that will work for you.
If you want to watch the parade, a good place is the bridge area close to Adventureland. If you stand facing the castle, you can still see the parade, but the volume of the music isn't as loud as if you are by the curb and you won't usually have a lot of people around that might be annoyed by your son if he gets noisy.
Most people don't think of the Monorail as a ride, but your son might enjoy it. You can take the monorail to one of the monorail hotels, look around and then hop back on to get back to MK.
Hope this helps. It looks like you might have a full day at MK.
Ooops, almost forgot. In case he needs to rest, or you need to lay him down to change him, the First Aid stations at any of the parks are great. The one in MK is by the Crystal Palace restaurant.