I don't think it can be harmless. Surely the MM is regarding his wife with disrespect, contempt, and a lack of care by not letting her know something fundemental to their relationship that she believes to be faithful.
If she knew her husband was a liar and a cheat, she might make different choices about HER life. She might decide that she doesn't want to be faithful to him, that she wants an open relationship, or to 'turn a blind eye' and put up with his infidelity (whilst taking extra precutions against STDs). Or maybe she would rather be single or have the opportunity to have a meaningful relationship with someone else. We don't know what she would like, because she isn't being treated as an adult with a right to make informed choices about her own life.
This is causing her harm. It causes this harm whether or not she is ever aware of it. It is not the action of a loving husband and father who respects his wife. He is treating her as a lesser person whose job is to stay at home, put his children to bed, look after the house and dutifully await his return.
In addition, he may be exposing her to STDs, not casting aspersions on you in particular OP, but if he is having unprotected sex at home, he could be harming her, and who knows who else he is sleeping with too.
In order to justify this extramarital excitement and sex to himself, he may well be changing how he percieves and treats his wife. Deciding that she doesn't do enough for him and that therefore he is entitled to have his fun elsewhere. Maybe he's been criticising her, telling her that she's not fun anymore, that she's less attractive, etc. That would also be harm, even if she never finds out that the cause was an affair.
And then there is the spectacular hubris in assuming that the affair will never be discovered. Maybe some affairs arent - who can say? But a lot of affairs are discovered, there are plenty of threads here about women who have discovered their partner is cheating, there are lots of ways for that to happen. And others can infer that its going on from their partner's changes in behaviour even if they never get proof. Don't you think that those cheating spouses thought they were clever and discrete too? Just because he doesn't intend to tell her, doesn't mean she'll never find out.
OP, you don't know about MM's marriage, no matter what he tell you. There have been women on here who have discovered their partners/husbands have been having affairs while they were pregnant, undergoing IVF, looking after a newborn, undergoing chemotherapy, while they were caring for an elderly relative etc. I bet none of their husbands told thier mistresses the circumstances of why DW's attention wasn't on him every second of the day. How would it make you feel about him if you found that your MM was of this order of pathetic excuses for human beings? Not very sexy huh?