Re Georgiansilver's suggestion that the lyric is "the Minches" rather than "the Minch is" I don't think that is right myself.

There is an area of the sea called "The Minches" because there is more than one Minch. The larger wider channel which is between mainland Scotland and Lewis, with Skye to the south, is called "the North Minch" or more generally it is just called "the Minch".

Whereas the smaller strait between Skye and North Uist is called "the Little Minch" or "Lower Minch"

When folk talk about "the Minch" though they are generally talking about the former.