That's a good question. I would think you could do an experiment and "kickstart" the glands, by showering as usual, and then wearing a shirt that has nylon or mesh in the material (not pure cotton), and see if you just don't have any of that type of sweat, or if you are just extra-good at hygiene...
I've heard that antiperspirants with the chemical aluminum chloride, can be bad for you. But it's also in the genetics. It sounds like you're lucky! I can go a day without it, but it's a bad idea if I push it beyond that, LOL.
I'm blessed with dry feet.... I can wear the same socks and workboots for a week in a hot, humid Texas summer, and not have any foot odor at all. But for psychological reasons, I change socks every day. Other peoples' feet stink the second they get out of the shower, even if they wash & scrub with antibacterial soap, and soak in bleach.
Charles