cross, this is a by the book answer. your marriage is valid regardless of whether it was registered or reported. registration in the nso is not the basis whether a marriage exists, it is just evidence that it does. a marriage celebrated outside of the philippines is valid.
nevertheless, fruad requires a fraudulent intent. by providing a cenomar to retrieve the marriage certificate, i do not see this as an act punishable by law unless there is a fraudulent intent to cause damage.
however, if you place single on a public document, and it is material, then there is falsification.
foreign marriages and divorce are quite tricky. your husband has to be an alien and be the one to acquire the divorce. it is not automatically recognized here but requires you to have the fact of divorce proven in court.
the not so by the book answer is if you are able to retrieve your marriage certificates then there is no longer any evidence here of your previous marriage.