Rifles get the romance, and smoothbores get the bulk of the work done.
Kind of the difference between Special Forces and regular infantry. S.F. gets some crazy, story worthy, gutsy, stuff done, but, as was said or written I forget where, "it is the regular troops that take the ground and hold the ground they take."
Rifles in that area at that time seem to have been more common than in other places. "Dikert" guns in various spellings get mentioned a few times in period writing. Almost any rifle style of that time period from places in Pennsylvania, Virginia, maybe Maryland and maybe N. Carolina,,,, that settlers would have come from would be possible.
Maybe someone better versed than I can list styles available to us now that would not be appropriate. Process of elimination might narrow the field, and thus the discussion.
A smooth bored, rear sighted, Type-G/Carolina trade gun would also be possible. As would many other fowling piece and musket options.
I've often wondered about the period accounts of Kings Mountain and other events in the area at that time regarding their mentions of rifles. We're rifles mentioned specifically because rifle ownership and use was still mentionable, news worthy if you will?