Fowler reckon's that Minch is probably from th Old Scandinavian "megin nes" = great headland.

I don't see it myself: the Minch is a *channel*. Both the Minch and the Little Minch are surrounded by headlands, but from a boat no one of them stands out as being particularly "great" compared to the others. And in any event sailors are not prone to naming water features after nearby land features, or vice-versa. It just sounds like someone who hasn't been able to find a plausible etymology clutching at straws.

It also seems odd that the Minch features at all in the song, seeing as Mingulay is actually in the Hebridean Sea, with a hell of a pull even to the south end of the Little Minch...probably much further than local boatmen would have normally gone back when the island was inhabited...just one more indication that the song was written by someone outside the community.