There is an exception for CCDW permit holders I believe.. Section
1448B(C)(6) I think it was.
(6) Transactions in which the potential purchaser or transferee holds a current and valid concealed carry permit issued by the Superior Court of the State of Delaware pursuant to § 1441 of this title.
As I understand this, as long as the person purchasing the firearm has a valid Delaware CCDW permit, a face to face transfer can still legally take place without going through a FFL. I'd suggest having a good, clear copy of both the buyer's Delaware CCDW permit and Delaware drivers license for your records.
I'm not a lawyer and hate legal text. Hopefully someone else can verify this or correct me.