My DD is 16, and was just diagnosed (finally!) with Ehlers-Danlos Syndrome. She tires easily, and her joint pain had gotten much worse over the last year.
She used a stroller longer at Disney than most kids do (even at age 8 I brought one from home to use at Disney).
This past trip in March, after our first half day at Epcot (we got there in the afternoon), the next morning, she said her ankles hurt and her shoulder (and most other joints) and she didn't want to walk much that day. I asked her if she needed a wheelchair, and her eyes lit up with, "Can I do that, really?". We rented one at the parks, and she was so much more comfortable! Her friend was along with her brother and mom (it was just me and DD in our room that trip), and her friend was totally cool with taking turns often when we were all together pushing her.
That trip, I noticed so many "seemingly" healthy folks using rental chairs. It was in the 90's every day, so quite hot to walk the average 8 miles many days we were walking!
I didn't care if anyone thought it was wrong that she CAN walk but needed the tool to get her around. We'd park it upstairs at the Land pavilion and walk down to do Soarin' or eat or whatever.
She didn't care what anyone thinks, but she's that way.
I don't understand that your son would worry about what strangers think. Who cares? You have to do what's right for you.
This trip coming up next month, we're debating renting daily at the parks versus renting from an outside company the whole trip (which is where I'm leaning). We will eventually buy a good lightweight one to have for trips with lots of walking, but it takes time to research what we need.
I say if you need it, bring it and tell him you need some help pushing you. You can always take breaks.