There are a number of scottish songs which I enjoy hearing, but I would never perform them myself because I cannot sing them in Mock Scottish. For me it does not work.
I know singers who are dialect chamelions. If they sing a song from Ireland it is in a stage Irish accent, if a Scottish song, a fake Scots accent. I personally find listening to the performance grates upon my nerves. In some cases it may be a question of degree. Some singers have a sensitivity to songs which allows the to perform them without turning them into a mockery of their subject.

My view is - If you can keep true to the spirit of the original, it may be acceptable. If you are simply creating a mocking stereotype, leave it well alone!
Geoff!