I don't think the problem is using the Scots words. There is no need to change those. However I think it would sound better singing a Scottish song by singing the Scots words in your own accent or at least some kind of more neutral accent rather than going overboard and trying to mimic a full blown Scottish accent. When people mimic a Scottish accent they do tend to go over the top and it does tend to end up quite comical and can be cringeworthy. Plus if Americans do it for some reason it often ends up sounding like some kind of mock Irish accent. In my opinion anyway. Whereas reasonable people will be accepting to anyone attempting the Scottish words themelves.