Will shaving my armpit hair reduce body odor?

It might. Armpit hairs can slow down sweat evaporation and trap oils and smells. But even if you shave closely, if you don't keep the armpit clean, you can have an odor. Some people also need a deodorant or antiperspirant to keep odors down. I personally think some odor is natural and that we tend to get overly concerned here in the usa.