I don't think it's necessary to tell her she can reach you by cell phone. She already knows that. Just say you're going out. If she asks what time you'll be home....you don't know. If she asks where you are going....you're not sure where you may end up being. The point is making yourself unavailable to her.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!