No. Nuclear weapons release authority belongs to the President of the United States or his constitutionally designated successors if the President is dead or unavailable.
In the good old days of yore, some National Guard units operated Nike-Ajax. However, the officers in command of those units were Regular Army, the weapons were owned by the AEC and entrusted to the regular US military custodial units, and the Guard units were on permanent federal callup for the duration of the mission.