Nothing contained in § 16-40-11 through § 16-40-13 shall be construed in a manner as to interfere in the operation of any secondary schools that were in existence on May 7, 1941, and which had been approved by the director of education or of private schools or institutions of learning in this state properly registered at the office of the department of elementary and secondary education or the office of higher education and which have been approved by the board of regents for elementary and secondary education or the board of governors for higher education.