It's important to realise that people are all different physiologically. Some people suffer from sweaty palms, others don't have this problem at all.
Sweat itself is pretty well odourless. But it supports bacteria which multiply and, after about 30 minutes or so, give the characteristic 'sweaty' smell.
A few years ago, after running in a wet field, my running shoes were muddy and covered in grass, so i put them in a plastic bag inside my sports bag.
The next day, when i opened up the plastic bag, the smell was disgusting - the bacteria from my feet had multiplied in the damp, humid conditions i'd so kindly provided!
So - dry your shoes quickly and certainly don't put them in your shoe bag while they are even slightly damp. Charcoal inserts ("odour-eaters" in Europe) will help, but they take up valuable shoe space.
And yes - men can appreciate foot problems - we have them too