Sadly this is a tricky one, and a good example of statutes being written as clearly as mud. The CCDW permit affirmative defense for a charge of violating 11 Del. C. Sec. 1442 (carrying a concealed deadly weapon) applies ONLY to that specific statute. The nearest example I could think of that coming into play is if perhaps you were out and about, without your credentials on you for some reason or another and happened to have police contact that led to discovery of your concealed weapon. That being said, 1) you should not be engaging in any activity that would lead to police contact, and 2) if said police contact were the result of someone calling in a tip about a person carrying a gun, you're not doing a very good job of staying concealed.
That said, as far as school stadiums that are not directly on campus (the sports field at Sallies and across the road for Tower Hill come to mind) would more than likely still fall within the ambit of Section 1457 if it is affiliated with the school. As for stadiums etc. that are part of non-school property and not associated with a school system but are instead considered DNREC properties, the Delaware Supreme Court in Bridgeville Rifle and Pistol Club Ltd. v. Small, 176 A.3d 632 (Del. 2017) made clear that State AGENCIES are not authorized to adopt any regulations that are inconsistent with the state constitution. This case invalidated the ban on carrying firearms in State parks except for during hunting season and in designated hunting areas. The Kent County Superior Court further reinforced this when in Delaware State Sportsmen's Association v. Garvin, 196 A3d 1254 (Del. Super. 2018) that DNREC's designation of campsites and lodges as "sensitive areas" did not pass intermediate scrutiny. Post-Bruen, this case would largely have been decided in the same manner, but the field preemption issue may have been decided differently since intermediate scrutiny has been kicked to the curb.
With respect to any other offenses that relate to carrying of firearms, the specific statute itself typically spells out the permit defense, however, when it does not or when in doubt, err on the side of caution, especially in our quasi communist state.