I'd say he would be more relieved if nobody ever found out. Unlike with hiding a crime, or equivalent, there's no way an outsider would suddenly learn of it, out of his control. It's also not really something he would need to feel ashamed of, especially if he tries to be as good a son as he can. He wants to live his second life without regrets, so why mar it with his past life full of regrets? Not to mention, like I said, he would actually hurt his parents permanently if he told them. Their relationship wouldn't be the same anymore. I simply see no benefit in telling them but plenty of disadvantages.