If your W doesn't think sex and love have anything to do with each other, then why don't you suggest that you stay married to her but have sex with someone else? If they have nothing to do with each other then why would you love her any less just because you were getting action elsewhere? According to her philosophy, this should be just fine. You should call her bluff. Tell her that you don't believe that she thinks sex and love are unrelated. Tell her that her tr belief seems to be that one can only prove true love through heroic acts of celibacy, therefore she is linking love and sex more strongly than the average garden variety HD. She wants you to slay the dragon of your own sexuality in order to win the princess.
The reason you don't want to have an affair is that you believe that sex and love do have something to do with each other. You could tell her this.
The trust issue is a red herring in my opinion. Why don't you try using her brand of logic regarding this issue. You could say "If I thought you could lose your trust and sex drive over such minor issues than we might as well end it now.".
"Tell me, what is it you plan to do with your one wild and precious life?" - Mary Oliver
