I would tell her and risk divorce
I would not tell her and risk her life
I figure those guys don't really care about their mates anyway. So, if they confess, it's purely to ease their consciences.
There was only one time I was ever tempted to cheat on my wife when I was married. I got to know a brilliant and beautiful landscape architect, and every time I saw her we were just so locked in on each other that the word "chemistry" doesn't even begin to describe it. One time she suggested we have a drink, and although I was tempted to say "yes", I hesitated for a bit and said "no". I just couldn't cross that line that I know had such a temptation to ruin my marriage.
Of course, if I had known then what I know now I just might have said "yes", but that's another story. What counts is that I cannot really answer the question because I cannot see myself doing it.
"you're better off on Stormfront discussing how evil brown men are taking innocent white flowers." Infinite Chaos
Otherwise, the partner who cheats and feels guilty, shameful, etc...too bad...there's absolutely ZERO reason to dump one's indiscretions on the other. Talk to a therapists or spiritual leader...or anybody but the other spouse...IF YOU WANT TO KEEP A MARRIAGE. The unknowing spouse will be harmed over a senseless confession by a guilty spouse...and that is way more inhumane.