Further up the page in a follow up reply, you mentioned a steady rest needed to do this and that's something I thought about when I read this first post, because it takes a pretty large diameter dowel to make a "short starter" that will just fit inside bore of most smoothbores we use.
At first I thought about drilling a hole through a wood board the same size or a little larger than the diameter of the dowel - to use as a steady rest . But there may be an easier way to do it since the length of this dowel won't be anywhere near as long as a ramrod.
Taking a cue from a wood lathe, one might use a center punch and indent the center of the dowel in the opposite end from where you put the screw in. Then hold the center punch in a vise and press that end of the dowel against the point of the center punch while turning the dowel slowly with the electric hand drill. That would also free up one hand to file or sand on the dowel as it turns.
Gus