A note addressed to the executor: who's that?
My mother has a solicitor but I wouldn't expect anyone outside the family to know her name. In fact, if they did find it out, I'd feel a bit creeped out by that.
Actually, it's so raw I don't know who the executor is. Is it the solicitor or me or my siblings or a neighbour? We haven't gone into it.
Something saying: Dear Executor would jar with me whereas a note saying something like: 'Dear Limited and family, I am so sorry for your loss.
I've agonised over this and if you feel this is wrong please accept my apologies and ignore me.
But I knew your mother [insert anecdote] and liked her car and I would like to offer a good price for it.
If that's what you would like, I'd like to meet. If you don't want to, I understand. I'm sorry if I have offended you. That was never my intention.'
They'd get more brownie points for sending a wreath. But I'd be checking as to how close they really were because I am my mother's daughter 
However, at the end of the day, my mother was a really practical woman. She'd have taken the best offer and would have wanted us to as well.