Yes - be aware that the big scam in car buying these days is to send a fake cashiere's check. So get a check from a big bank and call that bank up to verify its one of their checks.
Wire transfers are much cheaper than they used to be because the electronic communications network is cheaper. So you could ask for a wire transfer directly into your account and it would only cost about $7.50 or so in fees (at my bank anyway).
I don't think there's much chance of a fake wire transfer.
Ken300D