Your barber is a beauty, although I'm not certain of it having been dipped, or not. That is probably only certain with the coin in hand.
If you have a Local Coin Shop near you, see if they submit coins to NGC or PCGS. If they do and they are anywhere near ready to put a shipment in the mail, it will be much cheaper to do it that way, even if they charge you a small fee.
Both PCGS and NGC charge a invoice fee and a transfer and insurance fee so that a single coin may cost you close to $60 to send in all by itself.
Plus, a local shop will be able to give you an opinion on cleaned or not cleaned.
It's worth the gamble on that coin to send it to NGC all by itself, but you might find a slightly less expensive way to submit, other than a single coin. $30 (over $300)+$21+8 = $59 for that coin by itself to NGC, I believe.
Or you can send it to me and all your troubles about it will be over
