It shall be unlawful for any person to operate a dredge for the purpose of catching, taking or harvesting conchs over leased shellfish grounds, natural oyster beds or other areas declared closed to dredging for conchs by the Department by regulation; provided however, that those conchs of legal size taken by a person on a vessel with a valid oyster harvesting license or a person with a valid commercial clam dredge license while engaged in lawful dredging operations, whether or not over leased shellfish grounds, natural oyster beds, or other areas declared closed to dredging for conchs by the Department, may be retained for noncommercial purposes. The Department is authorized to promulgate regulations that close areas to either dredging or potting for conchs.