The classifications of municipalities as first-class cities, second-class cities, unclassified cities, and towns, and the restrictions, limitations, duties, and obligations specifically imposed by law upon such classes of cities and towns, shall have no application to noncharter code cities, but every noncharter code city, by adopting such classification, has elected to be governed by the provisions of this title, with the powers granted hereby. However, any code city that retains its old plan of government is subject to the laws applicable to that old plan of government until the city abandons its old plan of government and reorganizes and adopts a plan of government under chapter 35A.12 or 35A.13 RCW.