Go for it. There will always be one or two people to carp but don't let it get to you. I've sung American songs all my life because I love them. And I sing a lot of songs on cajun French because I love them too. Not to mention Caribbean songs. I'm not really aware how much of an accent I put on, but as I'm lousy at imitating accents they're probably terrible. probably terrible. But people don't generally walk out, or throw rotten eggs. I went to the USA recently for the first time, and I asked a couple of friends how it would be if sang American songs. They said "go for it" to me, and I did. It was fine. So I pass on the same to you.
   I'm from England, by the way.