Richie - Have you heard the 1938 recording of Warde: As The Dew Flies Over The Green Valley" (LOC). He pronounces it doo

The same pronunciation is used by Reba Dearmore in the version Jenny, Fair Jen (Max Hunter).

In both cases the word is given in print as dew. And Bronson remarks on this being a characteristic 4th line of the American group C tunes. Whether it's an American rendering as dew of an original Scots doo, I wouldn't like to say; but it's not impossible. (And it makes better sense of the line!)

Mick