I suppose he could have. Bush's papa banned imports of various guns by EO. But notice that even BJ Clinton didn't try anything so bold. Republicans can get away with that sort of thing, Democrats didn't use to be able to.
Bill didn’t have to because the ban was in effect and didn’t expire until Bush was elected. The question was what would Gore have done, and an executive order was my bet if a bill was not forthcoming preserving the AWB. Remember too, the Dem’s learned that “Gun Control” was a loser; we need to reinforce that fact every chance we get!!!