one of my ancestors, I think my great grandfather and possibly his father before him? was a dry stane dyker in Angus.
He / they were responsible for all the walls on the Lindertis estate and perhaps wider afield. He - or his father - built the cottage in which the family lived for several generations near Kirkton of Airlie.
No songs passed down that I know of -- - having done a very little of the craft myself I am not sure it lends itself to singing while you work? Not regular/rhythmical activity- -needs some focus on the size and shape of stones required and then finding them from the available ones spread out waiting to be selected. The walls I learned on during the various courses I attended were all double sided with infill between so did involve more than one person (quite a number when on a course!) - a partner working the opposite side and assisting with the 'ties' that linked both sides at certain points, also the coping stones on top.
The smaller hands of children and women in the family would have tucked all the little infill stones and pebbles into place, making sure not a chink of light could be seen through the wall!