I've so far found two versions. One is a Scots Language version, which is the one in the DT. There seems to be a version which is essentially English.

Perhaps you could have a look at these and see if any are close? How much of a difference is there between either of these, and the one Andy Stewart sings?

Muckin' o' Geordie's Byre
Lyr Add: Muckin' o' Geordie's Byre - Mudcat Forum Thread
Muckin' with Scots Language Dictionary
Muckin' o' Geordie's Byre ~1700 - Scots
 
Jean Redpath's English Version
Scottish Radiance's English Version