I have much the same condition, only with me I was just born that way. I sweat VERY little, and can go down in the blink of an eye when I reach my limit. The heat and humidity of growing up in South Louisiana were a constant challenge to me, but WDW *still* got me with heat exhaustion the first few times I went in summer.
It took me several visits to get my WDW routine down, but I now have a system that works pretty well for me.
Clothing, etc.:
-A good sunhat is a must. I wear a Vineyard Haven from Watership Trading.
-Sunglasses at all times when outdoors in daylight; this wards off headaches. Wear them on a string so that you don't have to put them away when not on your face.
-Misting fan. Get a good one (I like the ones from O2Cool.) Fill it with ice when you pass a drink vendor's bin; they will let you take it for non-potable uses, and you won't have to stand in line.
-Light-colored clothing. Forget the black and navy and wear nothing darker than khaki. Wicking fibers will evaporate off water that you pour/spray on yourself, cooling you down fairly quickly. Cotton knit just gets sodden, especially underwear -- invest in some sport underwear.
-Water sandals. These let you wade into the fountains and cool off with the kiddies. I also found that the amount of concrete in the parks makes the area just above ground quite hot, so keeping my feet/legs cooler was very helpful.
-Cloth diapers. (I know, but try not to laugh). It doesn't HAVE to be diapers (can be washcloths or just pieces of cloth), but I've found they work better than anything else for the purpose. I buy a pack of plain birdseye flat cloth diapers, and carry a few of them in a gallon-ziploc in my bag. They are super-absorbent, thin enough to tie in a knot, and fairly large. If I feel myself getting into trouble, I have DH go to any vendor and fill the bag with ice, then soak the diapers in ice water to apply to my pulse points. I can tie them on at the elbow or on my neck if I need to.
Behaviors:
-Stay onsite and Park-hop. Go to the first park to open in the morning, and try to leave by 11:30. Stay indoors or in a pool until about 4:30 pm, when it's fairly safe to head back to a park, then stay until late closing. Take advantage of EMH to get as much night park time as you can.
-Make it a point to walk on the shady side of the street, and cut through shops when possible.
-Drink a LOT of water (which kind of goes without saying.) Add in a sport drink in the middle of the day if you're feeling down. Eat some fresh fruit, too.
-Eat VERY frequently, about once an hour, and carry around protein snacks. (I find that nuts with a slightly sweet glaze work really well as an emergency snack.) Be sure to eat protein at breakfast and go easy on the carbs.
-Use a lot of the strongest barrier-type sunscreen you can get. The spray works best for me. On a hot day I put it on any time I feel my exposed skin getting noticeably warm, which is normally about once an hour. (Those of you who sweat normally probably don't feel this much, but people like me literally begin to feel like we are on a griddle when direct subtropical sun hits our skin for more than about 10 minutes.) I like the Bullfrog formulas that contain Titanium dioxide. Higher SPF than 30 doesn't really do much better in warding off sunburn, but my personal experience is that it does help with keeping your skin temp down, so I like to use 50+.
Lastly, don't hesitate to call First Aid if he starts looking pale or acting confused at all. Have him sit and cool his pulse points while you wait. Any CM can call First Aid for you; just grab the first one you see.