If imitation of an accent is a problem, then -- rest assured -- the audience will also have a problem.

I'm with Jim Carroll's earlier post on 14/6 which suggested that adaptation of text into local pronunciation could still produce a good version, although both he and Tattie Bogle (later) also addressed the problem of dialect words.

IMHO some are too valuable or special to be denied -- TB mentions Adam McNaughtan's song 'The Yellow on the Broom' (based on Scots traveller Betsy Whyte's volume of family reminiscence) in which he uses her traveller cant for townspeople or settled folk -- scaldies: the whole sound of the word in your mouth is an expression of the sentiment of the verse and any replacement with something like 'townsfolk' would weaken the whole verse. So I'm with Jim's suggestion of a few judicious glossary notes in advance.

Mind you, not sure where that leaves me when one of the songs that speaks most to me is in potentially impenetrable North-East Scots Doric -- 'McGinty's Meal an Ale', by George Bruce Thomson. I first came across this in Norman Buchan's Ballads Club at Rutherglen Academy somewhere between 1958 and 1960 -- we heard it on a field recording and one of the lads in the club took it up so enthusiastically that we all roared out in the choruses and gradually picked up the sense of the narrative (a pig escapes during a rural celebration and accesses the drink-- after which he creates chaos rampaging through the house before finally being carried out - drunk - upon a shutter). But there was never a notion that words, in this particular instance, could be changed.
In fact, at last January's Celtic Connections there was a concert to celebrate the re-print of Norman Buchan's '101 Scottish Songs' - originally published in 1962 - when 22 singers came together to perform songs from the book and the celebrated bothy ballad singer Hector
Riddell sang McGinty's: on the accompanying DVD put out by the TMSA, you can view participation from the onstage performers (myself from near Glasgow and Margaret Bennet from Skye) joining in delightedly on the line about Mrs McGinty's distress -- 'An she let out a skirl that wad have paralysed a teuchit', where 'skirl' is a scream and 'teuchit' is a lapwing or peewit.
But it's providential that we both have Scottish vowels and the ability to produce a 'ch' sound… and also that we understand what the dialect words mean.

Not sure how much my meanderings have helped, but I have to come back to Jim Carroll's point (made either here on on another post) that an understanding of the song is the most important starting point -- if a singer sings from the heart then neither accent nor dialect should be unsurmountable problems.