Scotch is the correct pronunciation among the Scotch-Irish of VA, NC, SC and TN. It’s a linguistic throwback, like many unique words in the foothills and mountains here. I’ll stick with their name for themselves, personally.
Another linguistic oddity pertainining to the Shenandoah Valley, would be that up is down, and down is up. If you’re going down the Valley, you’re headed toward DC. If you’re going up the Valley, you’re headed toward NC. It refers to altitude instead of north and south.
The “up” - “down” usage survives where I live. When someone says, “I live up Clear Fork,” than means he resides upstream of the confluence of Clear Fork and Wolf Creek; in this case, again, “up” being a southerly direction.
Like the Nile ... up is down.
Looking back at comments on this thread and elsewhere, there does seem to be a north-south divide on the name issue. The Scotch Irish of the Shenandoah Valley appear to always have called themselves Scotch Irish, but in the north the terms often used are Ulster Scots (traditionally) and Scots-Irish (more recently).