Mairi (MAH-ree) is not Gaelic, it's a Scots approximation of the Gaelic "Mhairi", where the "mh" is a sound between "b", "m" and "v" which doesn't exist in English. The subject of the song (who died a few years ago) called herself "Mairi" though.

The song is excruciatingly tacky and must have been the topic of a zillion threads here.

I'd bet you'll have an interesting time trying to pronounce "Dalziel".