How your voice comes out of your mouth is almost inevitably coloured by how the song came into your ears. It's remarkably hard to avoid that even if you try hard.

It'll also be coloured by the other songs you've learnt and sung. And all that adds up to your own voice.

What sounds silly is when you go overboard trying to imitate the way someone else sings it. Especially when you can't keep it up when the song is done and you are talking.

A mid-Atlantic accent? That should be reserved for singing whale songs.