When I sing an Irish or Scottish song, I leave in the dialect words thay simply have to be used, if they are needed to rhyme or would just sound funny if changed, and I tend to change the ones that are possible to English. I automatically fall into sort of an inflection rather than an actual accent, so hopefully it doesn't sound like I'm faking it badly, but rather acknowledging the song's origen. I once sang a funny Irish song that way, and afterwards an Irishman came up laughing and told me I'd just transported him back to Belfast (!), so I guess it doesn't come out too bad.

Andy Irvine tells a funny story about his youthful Woody Guthrie period, when he sang with an Okie accent. He met a girl early in the evening and spoke to her that way, not realizing they would be spending the evening together. He had to keep up the fake accent for hours. Along the way they ran into a cop who looked on young Irishmen with suspicion (they were in England), and what's more, knew Andy. The cop's face when he heard the Okie accent was something to see.