That is a good question, and you should not delete it. If sold by Etsy exposure you should complete the sale. This is to make sure you are operational inside of Etsy's TOS and not setting yourself up for fee avoidance.
I personally would ask the buyer to act as if they are checking out online--they can hit purchase, but just not pay via paypal. They have the option to check off the MONEY ORDER or CHECK tab which indicates they will be paying you other methods than Paypal.
Once the sale goes through, they can square up with you in cash. You then mark the item paid in your seller console and / or shipped.
You will still have that small fee owed to Etsy for selling fees, but now you have a sale in your shop and can get feedback. What's not to love?