Well . . . I often sing "The Diamond Ship," the 4th verse of which just does not rhyme in my own generic Ammurican accent, but which does rhyme in Scots. I generally sing it in my own voice until I get to the 4th verse, and then sing it with just enough Scots to make "home/hame" rhyme with "name." I feel uncomfortable singing it without even a nod to the Scots rhyme, and I also feel uncomfortable singing the whole song in what I am sure is a terrible faux Scots.

If it makes others feel uncomfortable the way I do it, well, they can go out for coffee while I sing. (grin)