I'm not real well versed in these things... so take it for what it's worth... but....
a state of emergency CAN be used to suspend rights... typically it's used to allow administrators the ability to make quick decisions regarding public safety, etc that would normally have to run through due process. A step further than that would be martial law, at which point the military could be activated on our own soil essentially.
With all that said, just because a state of emergency is declared, that doesn't immediately mean all of your constitutional rights are suspended. It doesn't mean all of a sudden you aren't allowed to say what you want, own or use weapons, or anything else... Unless of course the decision is specifically made to suspend those particular rights.
Otherwise it would have to be something already established in the Delaware code. While I'm not a lawyer or anything like that, I am at least fairly familiar with the firearm laws in DE and to my knowledge there is absolutely nothing contained in them which denotes special treatment during state of emergencies, etc...
