Cornwal

[Paul Henry]

Still continuing with clan associations
snip her ancestors were from County Cork and the nearby County Armagh. I assume this would likely make them Ulster Scots. snip

I can't help with your clan question. but County Cork isn't nearby County Armagh, they really are quite far away in both geographically as well as politically(in terms of Country)
But if there is County Cork in your history it is very unlikely that your family could be called Ulster-Scots, ....different countries and different religions