I use coconut oil on my face and body, the same I cook with ;-) and it seemed to affect my fast so I stopped and can tell a difference. It dawned on me the large amount of oil I was using on my body was absorbing.
The bad breath is just part of it. If I will be around people I use dry baking soda and am careful not to swallow and rinse well, it freshens great but otherwise I just skim a wet brush through my mouth and hit the young hard. Good luck!