If you've tried deodorants and found they irritate your skin, consider washing with an antibacterial soap such as chlorhexidine (Hibiclens), or applying an over-the-counter antibiotic ointment. They'll annihilate the bacteria on your skin, making it harder for the survivors to reproduce fast enough to cause odor problems later in the day. For added protection, sprinkle on some baking soda or talcum powder. Both do a good job of absorbing moisture from the surface of the skin. You'll get deodorant and antiperspirant protection using a one-two punch that's gentle but effective.