Whenever during the recess of the Legislature charges shall be preferred to the Governor against the Comptroller or Treasurer, for incompetency, malfeasance in office, willful neglect of duty, or misappropriation of the funds of the State, it shall be the duty of the Governor forthwith to notify the party so charged, and fix a day for a hearing of said charges; and if, in the case of the Comptroller, from the evidence taken, under oath, on said hearing before the Governor, the said allegations shall be sustained, it shall be the duty of the Governor to remove the Comptroller and appoint another in his place, who shall hold the office for the unexpired term of the Comptroller so removed. However, if, in the case of the Treasurer, from the evidence taken under oath in the hearing before the Governor, the allegations are sustained, it is the duty of the Governor to remove the Treasurer, and the deputy treasurer shall act as Treasurer until the next regular or extraordinary session of the Legislature following the appointment, whereupon a successor shall be chosen by the Legislature who shall serve for the unexpired term of the Treasurer so removed.