From Jane Austen's Emma:

enjoying the youthful simplicity which could speak with so much
exultation of Mrs. Martin's having "two parlours, two very good parlours,
indeed; one of them quite as large as Mrs. Goddard's drawing-room;
and of her having an upper maid who had lived five-and-twenty years
with her; and of their having eight cows, two of them Alderneys,
and one a little Welch cow, a very pretty little Welch cow indeed;

So, at least in Jane's day, Welch was a legitimate spelling for the word meaning from Wales.

Bingley

Bingley