I did a bit of scrounging around in some of my boxes of unpainted lead, and was able to come up with the two necessary components I was looking for: An old Foundry Wild West gunslinger wearing a bowler hat(who also had a nice big mustache), and a pack of Harlequin Miniatures U.S. BAR Gunners.
I selected one of the BAR Gunners that was sculpted wearing a scarf, as I figured it would help hide the neck seam. After two quick head removal operations, I glued the bowler hat wearing head onto the G.I. body, and voila...a passable Dum Dum Dugan figure!