OP, we were in your exact same situation last year with our DS 3 who was basically the same height as yours. We were there for 7 days, hit all parks, and rode almost every ride with a 40 inch requirement.
1. We were never asked to take his shoes off
2. They were very strict with making sure his head hit the bar
3. The 40 inch bars are closer to 40.5 or 41 inches
4. Big shoes and double liners are the key
5. Don't listen to all those who will scold you for this tactic, the 40 inch rides are more than safe (It is not like this is RnR or Everest). We did Thunder Mtn, Splash Mtn, Star Tours, etc...
As for shoes, we used timberland work boots.
Kid loved the boots and they look good with pants on. Also used double liners by pulling shoe liners out of another set of boots. Only down side to the boots is they hurt when the kid kicks you, so if you plan on carrying him a lot or doing shoulder rides (or method of kid movement) be prepared.