Isn't one of the reasons for you wanting to fast so that you are no longer dependent on nicotine anyway?
As with any fast/diet/supplementation, you don't HAVE to give up anything you don't want to...chances are, you're going to ultimately decrease your cravings for nicotine and end up quitting anyway.
When I start a fast, I don't give up caffeine or gum right away. I still start my day with coffee if I feel like the juice won't get me through the morning but eventually I realize I don't need it and would prefer to break the addiction. Afterall, that's the whole point of fasting, right?