No, that necessitates a new law. Reclassifying a semi-automatic AR platform rifle as a NFA weapon is an entirely new law. EO cannot do that. That's up to the Legislative Branch.
I believe the justice department will disagree. OE can do a lot of things, clarifying a law and sometimes writing new law, it all depends on how it is written. The emancipation proclamation was an EO.
an EO reclassifying guns to the NFA would likely hold up because it is using an existing law as its basis. would it get challenged? You bet, would the scotus uphold it, I think they would by the letter of the law, they would. An outright gun ban would violate the power of the executive branch because it creates a new law. An EO amending an existing law would be permissible, they do it all the time. Every president has issued EOs, even GW himself.
Shortly after the December 7, 1941 attack on Pearl Harbor, President Franklin D. Roosevelt issued Executive Order 9066, directing the interment of more than 120,000 Japanese Americans, many of whom were U.S. citizens.
While highly illegal and eventually ruled as such and 20k reparations were paid to the people and estates of those interred, it was done with an EO and it took until the mid 1980s to get it ruled illegal. By that time, damage was done.