Margaret and I, being Midwestern US, sing a lot of material from other parts of the english speaking world. We do them in our own voice, out of respect to where the songs came from. There are, indeed, some songs we can't do because of some dialectic things that would sound ridiculous in our midwestern accents. Early on, at an open stage in Chicago (about 20 years ago), a young singer from Glasgow got up to sing. Two of his songs were covers of Woody Guthrie,sung in what he believed to be an Oklahoma accent. My opinion is that you should feel the songs strongly enough to sing them in your own voice, whatever that may be.