Weapon choice is a confusing and convoluted issue, but just about the only certain thing you wouldn't be able to go with would be a naked fist. While boxing would come to have more acceptance as a gentlemanly pastime eventually, during the height of dueling, a physical blow was a bit no-no, and one of the things that could provoke a duel in of itself, rather than how a duel would be conducted.

By the early 19th century pistols were fairly standardized in the Anglo-American traditions, in large part because the way the duel was done was intended to minimize skill in favor of luck, as touched on here, but there were other weapons used at times. Those you could potentially refuse and request pistols instead, but a pistol you would have no ability to get out of based on that. I cover this more here. The short of it is that you could change a request for swords or shotguns to a request pistols, probably, but pistols to fists would almost certainly not fly, both because it would be ungentlemanly, but also of course because it wasn't deadly (enough), a big part of the duel being that one was hazarding his life to defend his honor, as touched on here.