Yes, that's right, the Minch is the body of water between the Outer Hebrides and the rest of Scotland including the Inner Hebrides. "How white the Minch is..." refers poetically to rough sea.

Mingulay is the 2nd southernmost of the Outer Hebrides and was uninhabited when I was in that area in the earlier 70s. I was staying on Barra, a few islands to the north, and I rented a car one day to drive Barra's 7 miles of road. From the highest point on Barra, I could see down to Mingulay.

This is a Gaelic speaking area, by the way, so I've always been curious why this song is in English. I assumed it to be a translation. Therefore, the difference in words has never bothered me. There is too some repetition of phrasing in verse and chorus which makes this short song more challenging to remember. This is the first time I've heard The Mingulay Boat song attributed to anyone and I'm happy for that information.

All the best,
Dan Milner