The way I read this, if you hold a CCDW permit, you can buy a firearm from an unlicensed person, same as before this bill was signed into law.
HOUSE BILL NO. 35
CRIMINAL HISTORY BACKGROUND CHECKS IN CONNECTION WITH THE SALE OR TRANSFER OF FIREARMS.
§ 1448B. Criminal history record checks for sales of firearms – unlicensed persons.
(a) No unlicensed person shall sell or transfer any firearm, as defined in § 222 of this title, to any other unlicensed person without having conducted a criminal history background check through a licensed firearms dealer in accordance with § 1448A of this title and 24 Del.C. § 904A, ...
(c) The provisions of this section shall not apply to:
(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.