I do not advocate lying to the cheating spouse. You lose the moral high ground. If THEY want to think things because you're looking good and smelling good, that's THEIR issue, and I don't think you should go out of your way to reassure them. But actively lying to them about another man for you?
Nuh-unh. Will it work? Sure, most likely -- but it's a "quick fix," and I just don't think it's right.
