You HAVE to tell his wife/ensure she has proof, even anonymously.
A close friend of mine was the wife in this scenario. She KNEW her H was cheating, but he lied to her face, in marriage counselling, to the GP.
She ended up in a really bad physical and mental state, on antidepressants, hair falling out, not sleeping etc, because she genuinely thought she was going mad.
She could SEE reality, but her H was denying it and telling her she was mad (as were his parents who bizarrely supported his second relationship, but not enough to be honest to the wife/rest of the world about it 🙄).
The truth finally came out when the OW had a child and she lived so close it couldn't be hidden.
A decade and a divorce later and my friend is still not back to the person she was. She still doubts herself, had to wean herself off the antidepressants that she never would have needed if he'd told her the truth from the start.
It absolutely wrecked her and I wouldn't wish that life upon my worst enemy, her H would have sent her to a mental health facility rather than admit the truth, it was evil.