No person shall conduct or participate in any competitive bicycle or moped race on any class I, class III, or class III-a highway or on the state-maintained part of any class II highway, unless such race is sponsored by a recognized bicycle or moped organization and the sponsor of such race has obtained, prior to such race, the written approval of the commissioner and of the police department of each city, town or place in which such race is to be held. In the case of a competitive bicycle or moped race on a class III-a highway, the sponsor of the race shall also obtain the approval of the executive director of the fish and game department. The commissioner and the executive director of the fish and game department may require insurance, police coverage or other regulations to insure the safety and protection of the public, and the permit may exempt competitors from such requirements of this chapter relative to rules of the road as are not inconsistent with public safety.