The administrative and executive powers of the county, including the power of appointment of all officers and employees whose appointment or election is not otherwise provided by law, are vested in the county manager, who shall be appointed by the board at its first meeting or as soon thereafter as practicable. The county manager need not be a resident of the county or of the Commonwealth. He shall receive such compensation as shall be fixed by the board. The officers whose election by popular vote is provided for in Article VII, Section 4 of the Constitution of Virginia, the school board and the superintendent of schools shall not be subject to appointment but shall be selected in the manner prescribed by law. The heads of all departments other than those hereinbefore referred to and excepted from the provisions of this section shall be selected by the county board. However, if a majority of the qualified voters voting in the election required by § 15.2-716 vote in favor thereof, then the heads of the several county departments, other than those hereinbefore referred to and excepted from the provisions of this section shall be appointed by the county manager.