Can US President reclassify firearms by executive order?
Is this feasible, and could a reclassification be done by executive
order (similar to the Executive Order on bump stocks)?
@user1167758 is not wrong in saying that "Executive orders are orders to the executive agencies to act in a specific way within the bounds of authority that congress has given them. They have no power unless they are backed by some law."
But, classification of particularly firearms in a particular class is one of the things that Congress has given the executive branch the authority to do within the bounds of the definitions provided in the relevant statutes.
An executive order is one means by which a new regulation is enacted. There is a process that has to be followed to change a regulation under the Administrative Procedures Act, but it can be done.
There are always a significant number of cases in which a firearm could legitimately be classified in more than one possible class and when that is the case, the executive branch has discretion to determine that a predecessor administration made the wrong call, if the new classification can be supported by rational arguments from the facts.
As a practical matter, regulations are updated and revised on a daily basis, and while past regulatory determinations aren't frequently revised, it isn't something terribly exceptional either.
For example, in the 1990s, the U.S. government decided that its historic regulations that is used for determining when entities were classified as partnerships for tax purposes and when they were classified as corporations for tax purposes, had become an unworkable, confusing mess that didn't advance legitimate policy goals and overhauled those regulations entirely.
Similarly, from time to time, the U.S. government updates lists of pollutants, endangered species, and controlled substances based upon standards provided by statutes and sometimes changes classifications used for that purpose.
This doesn't mean that any particular firearm is a good candidate for reclassification, and the question doesn't identify any particular firearm that would be reclassified, but surely there are some such firearms, and the bump-stock reclassification is one example of such a firearm.
For example, a Class 3 Firearm (per the link in the question) includes:
According to the NFA, a machine gun is defined as "[a]ny weapon which
shoots, is designed to shoot or can be readily restored to shoot,
automatically more than one shot without manual reloading, by a single
function of the trigger." This definition includes any frame,
receiver, or parts to make a machine gun.
Definition of "can be readily restored to shoot", in particular, is one upon which reasonable minds can differ.