There are some difference between 'traditional singers' (brought up in the tradition) and singers of traditional songs. What most people here are giving you are traditional singers. But there are also a good many 'singers of traditional songs' or revivalist singers, and the difference, in effect, is negligable.

I like to go back to old recordings where they are available (hopefully in some form that we can still hear), and so I'll get my plug in for my personal favourite - Joseph Taylor (long gone but not forgotten) and the inspiration for many revival singers, including providing the name for a fairly notable band! All right, he was neither Irish nor Scottish, but if you can find any of his recordings which date from about 1907 (some are on the Topic series I mentioned), I'm sure you won't be disappointed.

I hope you find what you're looking for
Les