I am in a similar situation with meds that I take for my medical issues. I was just at WDW earlier this month and found that almost every queue is covered or inside the a/c. I am trying to think of some that were not and I am having a hard time??
There will be a seperate WC/ECV line for most rides and attractions/shows. I didn't use them because I was stubborn and didn't get an ECV (but should have). I actually found relief from the sun/heat in most of the queues, especially at DHS and EPCOT.
My worst day health wise, due to heat and sun, was at AK. Although the queues for the Safari and the River Rapids are covered, they are not inside and have no a/c. And to me the park just seemed hotter than the other ones??

MK is another one that has less queues inside, but they are all covered.
I found the worst heat/sun issues to be while walking from ride to ride/attraction. I saw a few people with scooters that had a shade/awning type thing over the seat. You may want to look into that??
I hope you and your family have a great time.