First off, I really resent the idea that a DE CCDW gives such carve out protections. Doesn't comply with DE Constitution Article I, § 20 IMHO.
That said, I am not a lawyer - but if the park is not on school grounds or utilized as a recreation center, athletic field or sports stadium you should be able to OC there.
For federal law to apply it has to be school grounds:
[18 U.S.C. § 922(q)(2)(A)] does not apply to the possession of a firearm—
(i) on private property not part of school grounds;
State law is an adder after an offense is committed:
DE Tile 11, Ch.5, Sub Ch VII, § 1457 Possession of a weapon in a Safe School and Recreation Zone; class D, E, or F felony; class A or B misdemeanor.
(a) Any person who commits any of the offenses described in subsection (b) of this section, or any juvenile who possesses a firearm or other deadly weapon, and does so while in or on a "Safe School and Recreation Zone" shall be guilty of the crime of possession of a weapon in a Safe School and Recreation Zone.
(b) The underlying offenses in Title 11 shall be:
(1) Section 1442. — Carrying a concealed deadly weapon; class G felony; class D felony.
(2) Section 1444. — Possessing a destructive weapon; class E felony.
(3) Section 1446. — Unlawfully dealing with a switchblade knife; unclassified misdemeanor.
(4) Section 1448. — Possession and purchase of deadly weapons by persons prohibited; class F felony.
(5) Section 1452. — Unlawfully dealing with knuckles-combination knife; class B misdemeanor.
(6) Section 1453. — Unlawfully dealing with martial arts throwing star; class B misdemeanor.
(c) For the purpose of this section, "Safe School and Recreation Zone" shall mean:
(1) Any building, structure, athletic field, sports stadium or real property owned, operated, leased or rented by any public or private school including, but not limited to, any kindergarten, elementary, secondary or vocational-technical school or any college or university, within 1,000 feet thereof; or
(2) Any motor vehicle owned, operated, leased or rented by any public or private school including, but not limited to, any kindergarten, elementary, secondary, or vocational-technical school or any college or university; or
(3) Any building or structure owned, operated, leased or rented by any county or municipality, or by the State, or by any board, agency, commission, department, corporation or other entity thereof, or by any private organization, which is utilized as a recreation center, athletic field or sports stadium.
“I prefer peace. But if trouble must come, let it come in my time, so that my children can live in peace.” -Thomas Paine