With Obama's precedent-setting misuse of Executive Orders, Trump can just laugh at the survivors of the now defunct GOP and purge away.
I believe this is confirmation of that old saying "What goes around, comes around".
I ask this because every case I've come across involved an executive order that was issued under authority that was given to the president under a prior act of Congress.
Trust me -- the Republicans and Democrats will jointly pass veto-proof legislation stripping the White House of any such power if Trump decides to work on his own on this sort of thing.