This is one of those situations where one size doesn't fit all, which is why honesty with the counsellor is essential. There is no way the counsellor will betray that confidence.
Bear in mind this:
Some people cannot live with the guilt and it has a corrosive effect on both the individual, the relationship and the unknowing spouse. Some secret keepers stay in relationships for too long out of guilt, find themselves overlooking poor partner behaviour or if this isn't an issue, find that sexual attraction/intimacy is difficult because of the secret.
Some people forgive themselves for the mistake, learn from what led to previous poor behaviour choices and don't let it affect themselves personally, their relationship or the unknowing partner.
Some people find themselves in the same situation again more easily next time because the taboo has gone and because they did no work on themselves.
Some partners would rather not know if there was a one-off, never-to-be repeated act of infidelity and the relationship and both people in it aren't suffering any effects because of it. Fewer people (but they do exist) would rather not know about even serial infidelities.
Some people would rather know and be given the choice whether to forgive or end the relationship.
Most people don't have a clue what they would actually do if they discovered infidelity, despite previous certainty that it would mean the relationship was over. It is one of those situations when theory and practice rarely match.
Regardless of the very plausible reasons given for not burdening someone else with one's own guilt, one of the biggest reasons why people don't tell is not altruism. It's self-protection and not wanting to incur any personal losses.
Every individual and every relationship is different. Only you know your own character and behaviour though - in reality you might think you know how your husband would respond but you really won't until it happens, which is a big risk.