Well I'm a Scot by birth and residence but with an English accent, thanks to living in England for nearly 2/3 of my life. I lived in Suffolk, and there are not many people who can do a convincing Suffolk accent, either singing or speaking it, unless they've been brought up with it: otherwise it comes out as "mixed BBC rural". I do like the Kipper family repertoire as the Norfolk accent is close to it.
Having learned a lot of Scots songs since living up here, AND having been brought by a Scottish mother, I think I can make a fair stab at some Scots songs and the accent(s) and would never dream of trying Anglicise e.g. Yellow ( Yella, in fact) on the Broom. My mother taught us to say the ch sound properly very early on, no such place as LOCK Lomond! I also write songs, sometimes choosing to do so in Scots, depending on the subject matter if the song. But I'll never sound quite like someone who has lived here all their life. Like Allan Conn's wife, I often slip Scots words into conversation, especially wi' ma braider freens.
As for not mixing it, just look at Burns: plenty of examples of poems/ songs where he uses a mix of English and Scots in the same composition, even alternating versions of the same word between 2 "languages" - often for the sake of a rhyme.