polygraph for shame

My husband, of 11 years, had a 15 month long affair with the SAME woman he cheated on his first wife with 38 years ago. They BOTH claim there was no sex this time, but the other woman just lives 3 blocks away and from the text it looks as though they were physically intimate. My husband "can't remember" anything of their 43,000 daily text, 2,000 phone conversations and 200 pictures. He has been sober 26 years and has great shame in his life from things he did years ago. He is wanting to take a polygraph to prove to me that there was no sexual contact. My question is... Would his shame sway the test or will the truth finally be told? He denies telling the other woman he loved her...she says he did. I need him to take the steps that will open him up to what he did. I'm tired of him saying it meant nothing and it was just a game they were playing. I know that's not true.