First, I totally get feeling hot and uncomfortable, especially in a jacket and tie. I just have never considered "leg heat" to be such torture as to merit wearing shorts in town.
Alternatives would include loose-fitting chinos, or tropical wool or linen trousers. The worst possible choice is denim, which to me is very hot.
Completely agree.
However to answer your question: if you're already dressed down to wearing shorts, I think the footwear is immaterial... sandals/loafers/espadrilles/boat shoes/etc, wear whatever is comfortable. If you want to avoid wearing shorts, you need to invest in clothing that will perform well in the heat.
As someone who lives in New Orleans (which is the epitome of hot and humid starting about now and going until late September), you need to look into loose fitting, breathable clothing. For pants, look for loose fitting linen dress pants that will let any slight breeze cool you off and not feel so constricting. I just got a pair of high twist loose woven wool pants to see how they fare, that could be another option.
If you feel strongly about having a tie on, make sure the shirt is linen or some gauzy type of open weave cotton, and the jacket is unlined linen or loose weave wool/silk/linen blend. Personally, I'm leaning towards ditching the tie during the hottest months and drawing from 1930's/1940's daytime resort wear for inspiration: knit t-shirts/polos, camp collar shirts, short sleeve button downs etc. paired with an unlined and breathable jacket. You're still wearing a jacket, but with significantly less material covering your body and leaving more skin exposed to the air. Depending on the shoe and the pants I think you may be able to get away with no-show socks without loafers (like suede derbies or bucks), which gives one more place for bare skin to be exposed to the air.