The following are definitions of disorderly conduct. It's essentially a catch-all statue that the cops can fall back on if nothing else comes to mind.
0) Any act of molesting, interrupting, hindering, agitating, or arousing from a state of repose or otherwise depriving inhabitants of the peace and quiet to which they are entitled
1) Unlawful interruption of the peace, quiet, or order of a community, including offenses called disturbing the peace, vagrancy, loitering, unlawful assembly, and riot
2) Any behavior that tends to disturb the public peace or decorum, scandalize the community, or shock the public sense of morality
3) An offense which disturbs the peace and tranquility of the community in general
4) Intentionally causing public inconvenience, annoyance or alarm, or recklessly causing a risk, conduct that disturbs the peace or endangers the morals, health, or safety of a community
And finally, Delaware's statute:
A person is guilty of disorderly conduct when:
(1) The person intentionally causes public inconvenience, annoyance or alarm to any other person, or creates a risk thereof by:
a. Engaging in fighting or in violent, tumultuous or threatening behavior; or
b. Making an unreasonable noise or an offensively coarse utterance, gesture or display, or addressing abusive language to any person present; or
c. Disturbing any lawful assembly or meeting of persons without lawful authority; or
d. Obstructing vehicular or pedestrian traffic; or
e. Congregating with other persons in a public place and refusing to comply with a lawful order of the police to disperse; or
f. Creating a hazardous or physically offensive condition which serves no legitimate purpose; or
g. Congregating with other persons in a public place while wearing masks, hoods or other garments rendering their faces unrecognizable, for the purpose of and in a manner likely to imminently subject any person to the deprivation of any rights, privileges or immunities secured by the Constitution or laws of the United States of America.
(2) The person engages with at least 1 other person in a course of disorderly conduct as defined in paragraph (1) of this section which is likely to cause substantial harm or serious inconvenience, annoyance or alarm, and refuses or knowingly fails to obey an order to disperse made by a peace officer to the participants.
Disorderly conduct is an unclassified misdemeanor.
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It looks to me like open-carry does not apply to paragraphs (a), (c), (d), (e), (f), or (g). If you wanted to stretch it, paragraph (b) could apply in the "display" of the weapon, but part of your defense would be that you didn't do it to "intentionally causes public inconvenience, annoyance or alarm to any other person, or creates a risk". BTW, the police are going to have to produce at least one witness that said that you "intentionally caused inconvenience, annoyance or alarm to them", but even then, the charges should be dismissed.
Further, as long as you were legally carrying and in possession of the firearm, and weren't brandishing, they don't have a legal leg to stand on. I would not only get a lawyer to defend you, and after you're found not guilty, I would also have him file a suit against the city/county/state for unlawful arrest, harassment, and anything else you can think of. The only way we're going to get the LEOs to stop acting like the gestapo is to make it expensive for the city/state to back them up and to let them know we're not just going to lie down and take it.