Leviathan,
I don't think that there were actually too many whites here in the deep Appalachians prior to about 1790 or so. Settlement pattern largely took them through the Appalachians and on into Kentucky or the flatter areas of Eastern TN, and only afterwards, when the better land was taken, did they start working back into the hills. I have a hard time with geography, admittedly, so that might be a bit of an oversimplification, but that is what I have heard. Also, the whites in the SE-Virginia/Western NC/East Tennessee a settlements were more or less continually at war with elements of the Cherokee from 1775 to 1794, which probably had an influence on their choice of firearms.
So, I think a specialist bear pistol from the southern Appalachians prior to the 1790s is unlikely. The early Trans-Appalachian settlers did occasionally have pistols, but I'm not aware of any that can be demonstrated to have been made here that early.