Officers who are elected by the people, or who by the statutes are required to be elected by the city council, inspectors and clerks of election, one deputy in each department whose office was created and exists by reason of statute, the members of the board of school directors, persons enumerated in s. 63.53 (2), heads of principal departments of the city, all members of the law, fire and police departments, permanent or temporary technical advisers and experts employed by the board of assessment under s. 32.52 (4), one private secretary of the mayor, the appointees of the mayor under s. 62.51 and any other officers, clerks or employees in the service of the city whose positions, in the judgment of the city service commissioners, cannot for the time being be subjected, with advantage to the public service, to the general rules prepared under this chapter shall not be affected as to their election, selection or appointment by rules made by the commissioners.