The Red House first appeared in Playford, 1695. Scottish forms (Where Will Our Goodman Laye and so on) begin to appear from c.1750. On the whole the tune would seem most likely to be of English or Welsh origin rather than Scottish. Midis can be heard for comparison in the long John Peel thread: The Evolution of a Tune: "Red House" and "John Peel"

I think there's a fair bit of Welsh material in Playford, though it isn't always easy to tell; and of course a lot of tunes are common to both Wales and England, often under rather different names. Quite a lot of "Welsh Airs" were published during the 19th century, too, and you can get a facsimile edition of Davidson's Musical Miracles: Two Hundred and Fifty Welsh Airs for a Shilling from Llanerch Press, who also carry other printed material of Welsh interest.

Of course, the question was about recorded music. One place to begin looking is

Sain Records  (English language version)