Are there any Cowies in present-day Scotland who pronounce their name 'coo-wee' or 'kū-wē'? Or according to family lore and traditions, might they have pronounced it so in the distant past?

I am researching the possibility that American Coueys might be descendants of Scottish Cowies. In that pursuit, I am focusing on the pronunciation of the name rather than the spelling.

I understand most if not all Cowie Scots pronounce their surname, 'kaʊ-wee.' However, I know the name of the bovine animal called "the cow" (giver of milk and steaks) formerly was pronounced 'kū' or 'coo' in Old English. I also am given to understand that also is how it is pronounced in Lowland Scots. Which begs the question whether the Cowies who remained in Scotland, over time, might also have changed how they pronounce their name from 'kū-wē' to 'kaʊ-wē.'

The American Coueys came to the port of Charlestown (now Charleston) in the South Carolina colony from Newry, County Down, Ireland in 1767. Family records show they probably had lived in Ireland for at least one generation and possibly longer. So the ultimate question is whether the Coueys who came out of Ireland might have been descendants of 'kū-wē' Cowies who moved from Scotland to Ireland to work on the Ulster Plantation. Probably not a question one ever can know to a certainty but knowing whether the name is or once was pronounced 'kū-wē' would be a very strong clue.