> My experience has been that once I cool down and dry off, whatever smell there is drops significantly.
Different people have different bacterial flora on their bodies, determined by a whole range of factors, and exacerbated by the type of clothing they wear. It may be that your body has a 'benign' flora, that means you don't smell too bad. Others may not be so lucky, and they may honk.
Or they may wear Helly Hansen LIFA base layers...
I don't wear deodorant or antiperspirant, and I'm lucky that I don't stink too badly, unless I'm doing something where I'll be very anxious or scared. I usually carry a small atomiser of alcohol-based eau de cologne of some mild fragance, and give a squirt in morning and after I've had a quick wash.