Sorry, but you are wrong. The Secretary of Defense position is a creation of Congress and the duties of the Secretary of Defense are enumerated in Title X of the US Code. Nothing in the Sec of Defense's Oath of Office requires him to follow ANY order of the President, much less ALL of them.
Whether he follows orders of the President is entirely discretionary and then only when the order of the President does not violate his oath of office, which is to uphold the laws of congress and the Constitution.
Marlowe is correct. The SecDef is a civilian appointee of both the president and the senate. He is not military. He is under no legal requirement to follow the orders of the potus as are members of the military. The potus could, of course, replace him, but that isn’t really the point.
like I said, there’s the real world chain of command and your fantasy world.