Good find. Yes, under the 1862 law a city mayor could give orders in case of fire burning out of control (conflagaration) or other natural disaster. A slave rebellion or riot would also fall under this heading. Obviously in case of imminent peril the emergency would not allow time for a senior militia officer to appear on the scene and give instructions.

However, in time of war only a superior officer in a militia captain's chain of command could give directions. The examples you provided earlier indicated that General Lewis was in immediate command of volunteer militia within the City of New Orleans. If the Mayor is ever referenced in the OR, volume VI, I failed to see his name mentioned.