If you are focused on eating right and detoxing, after a while you should have no problem with this.
For the first several months I went without I had to shower twice a day and wash my under arms once or twice a day with plain water, but after the initial issue, the BO issue faded away even when I exercise.
I have been deodorant\antiperspirant free for over 18 months now.
I think I read a post a while back that coconut oil works...