To be fair, how would you come clean with your wife about this situation?
"Hey babe, my smoking hot co-worker has a picture of me "groping" her tits, and she uses it to force me to workout for her muscle kink. Please believe me!"
I think this is somewhat exaggerated.
It might be hard to believe and perhaps not all ways of laying out the facts will lead to the same reaction, but assuming she will either not believe him or still be offended no matter what he says and there is no way that leading with the truth would solve the problem is probably a stretch.
I understand why he might fear taking his chances, especially with trust between them being low at the moment. But that does not negate the possibility of another option than still hiding what's going on.
It's honestly probably still the better option to calmly explain the situation, because keeping up the act only makes things worse if she finds out later, let alone the fact that his silence doesn't really solve her suspicions anyway as this chapter showed.
If they hope to salvage their marriage, there comes a point where he needs to come clean and she needs to trust his explanation. Without either, their chances aren't good.