From what I understand, sweat itself does not smell. The odor is caused by bacteria feeding on the sweat. Those bacteria thrive in moist dark places that can maintain a certain PH level, on the acidic side I do believe. Our skin itself has an acidic PH, right? I’ve heard of the term “acid mantle” when referring to skin conditions. If the deoderant stones are salt based, it makes sense that they work to control odor. Salt is on the alkaline side of PH, and if the bacteria need an acidic environment to thrive, the alkalinity will kill them. Hair can compound the odor problem because it makes it harder to keep the underarm dry. Anti perspirants work by creating a dry, ph altered environment (the aluminum salts in the stuff mixes with the sweat in the sweat gland, and plugs it up) which is hostile to the bacteria, and it kills most of them off. Some/most contain bacteriocidal ingredients also wich are the actual deoderant. The fragrance is there to mask any residual odor caused by little bacterial survivors.
It sounds to me as if using the wipes after your warm up is a good idea. Simple washing takes care of most bacteria, no matter where it is on our body. The more bacteria you get rid of before applying an AP/D, the better it’ll work. Personally, I’d try to apply to the driest skin possible.
My personal product recommendation? Secret Solid. Keeps me dry, if my armpits are sweaty or damp at all it gives me the willies. And it smells nice, but not overpoweringly strong.