Was what the questioner did—concealing his wife's secret after discovering that the son was not his, and dealing with the situation with forgiveness and discretion—the correct thing to do?

The child is attributed to the husband if born six months after the marriage contract and the possibility of intercourse, and can only be disowned through li'an (oath of condemnation), based on the Prophet's (peace be upon him) saying: "The child is for the bed (i.e., the husband), and for the fornicator is the stone (i.e., disappointment/punishment)." Blood tests or DNA analysis are not relied upon to disown lineage. If the husband strongly suspects the child is not his, he is permitted to disown him through li'an. If the wife confesses to adultery and the husband covers her (i.e., keeps her secret), he has done well.