The laws governing the handling of classified information (not the exact charges in this trial btw) are largely sanctified via executive orders of previous presidents. The current president is still subject to following the executive orders of previous presidents, up until he rescinds, and/or replaces them. A president is not legally able to just ignore them, which is why rescinding/replacing executive orders of previous presidents is usually one of the first actions a new president performs. Trump did not rescind any EO’s protecting classified while he was president, in fact, he proudly strengthened them, instead, and was therefore subject to them.
President Trump had no more duty to “obey” an executive order issued by Barack Obama than he was obligated to wear Obama’s underwear that was left behind in the White House.
President Trump ignored prior executive orders whenever it suited him. He went through much of his tenure in office, for example, without nominating someone to fill a vacancy in the Associate AG post — which was never established by Congress, and was instead established through an internal DOJ order in the 1970s.
I don't see Smith appealing to any EOs to help his case, and I'm sure he would do so if they did.