Assuming that your son is over the maximum weight for the stroller by the time you travel, you could still try it, but I think you'd be exhausted trying to push an overloaded stroller around, especially if the added weight puts additional friction on the wheels, and overloaded strollers can be dangerous in that they're more prone to tipping. Also, if the stroller gets damaged, you can be held liable for the full replacement value (per the terms of your stroller rental agreement).
You could program the phone numbers of some rental companies into your phone just in case, and try and see how your son does without one. (FWIW, my 4-and-6-year-olds never needed a stroller, but also, we never toured without a nap break for more than 5 hours at a time, and were able to get them in bed at an early hour. YMMV, depending on the rigors of your daily itinerary.)
If you're sure you will need one (you know your little guy best), you can rent a double stroller directly from WDW, which holds up to 100 pounds (double the 50-pound limit for their single strollers).
https://disneyworld.disney.go.com/guest-services/stroller-rentals/
The double stroller is twice the width of a single stroller and has no divider in the middle -- shown here on the left, with single stroller on the right for comparison -- so it's perfect for a single, larger child, and would leave you some extra room and weight allowance, if you have other belongings you want to transport in or on the stroller.