I am only on day three of my fast, but honestly as long as I brush regular and drinking plenty of water, i have not had that much of a problem with bad breath, but then again everyones results of fasting are different for sure, and of course I am also still in the early days...
Whatever you use, becareful because lots of mouthwashes and gums have sweeteners in them, and artificial stuff, if your fasting you do not want to add any toxins to your system you do not need to.