I personally use and own an
ECV (also known as a
scooter).
Tell your son to think of it like this - the wheelchair is a TOOL, and nothing more. There are plenty of folks (not just at WDW, but everywhere) who use them. No, it's not fun to have to use one - but not using it could make the trip worse for your family, as it will limit your ability to stay in the parks and enjoy yourself.
A wheelchair - whether you rent one, or own your own personal one - is a tool. No different than glasses, a hearing aid, or a prosthetic. Period.
Would your son deny you the use of a hearing aid, if you could not hear? Would he deny you the use of a pair of prescription glasses if you required them to see?
You aren't using the wheelchair for any reason at all that is inappropriate. Rather, you are actually proposing to use it in the best possible way - not to avoid exercise, but merely to extend your ability to enjoy time with your family in the parks.
I have a family member who was extremely sensitive to how others would view our party when we would go out and about after I started using an ECV. He was - no kidding - absolutely CERTAIN that everyone was going to stare at us, and that we would become the center of a great deal of unwanted attention.
Because he was so uncomfortable, the first few times he went out with me (and the ECV) I told him to hang back, or stay off to the side. I encouraged him to do some serious people-watching, to see how others reacted, if he noticed anyone making fun of me, or pointing and laughing, etc. All of the things he was worried about.
So, reluctantly, he did.
And to his surprise, he discovered that me on my scooter was basically a non-event. The few people who do say anything, typically say it to me. And they are typically stopping me to ask where I got my scooter, and ask questions about the scooter.
At WDW, I'm even *LESS* of an event - there are SO many folks there using assistive devices of one kind or another - I'm really not a big deal. A bonus extra to using an ECV at WDW (or similar places) is that the chances that you will ever again see anyone from there anywhere else? Probably so tiny that you are better off betting on the lottery. Seriously. So who cares what anyone at WDW thinks about you - besides your loved ones - anyway? You'll never see them again.
Regardless of how you use the wheelchair - how much, or little - just use the tools at your disposal to have the best possible time on your trip!
Wishing you all the Magic you can find for your next trip