I would do as much as you can to pro-actively mitigate the heat risk for him. That might be certain clothing, wide brimmed hat, cooling towels, fans or misting fans, there are fans that can be attached to a scooter, alternating indoor/outdoor activities, time of day, always having cool beverage to avoid dehydration, etc. The
DAS will actually do little to mitigate the heat, possibly the opposite as it will put you
outside rather than inside in a queue. Shops can be crowded so he may find it difficult to navigate often with a scooter, dining locations often require that you purchase food, etc. so it can be hard to locate an inside spot to wait out a DAS return time.
You can certainly ask at Guest Relations. Keep the request specific to his non-mobility needs, even explaining how the scooter won't help that issue.
Enjoy your vacation!