Constitutional FAQ Answer #58
Q58. "I would like to know what the President can and cannot accomplish via an Executive Order. If Congress has NOT passed laws that mandate certain Administration policies which means that those policies are merely the result of interpretation of existing law then can the President issue an Executive Order that amend those policies, assuming the new policies do NOT contravene existing law. Would this be constitutional?"
A. An Executive Order can be issued by the President at any time to modify how any part of the Executive Branch does its job, or to modify how a law is implemented, if such power has been vested in the President by another law.
For example, I did a search on executive orders with the word Naval in them, and found one that transferred control of the Midway Islands from Navy control to Department of the Interior control.
Another establishes an Emergency Board to mediate disputes among various railroads, as provided in a section of the U.S. Code.
It is certain that an Executive Order could be unconstitutional. I'm not sure I get your example, but from the executive orders I have read, the power vested in the President by the Constitution or by existing law is what is used as the basis for the ability to issue the order.