Realistically, the US has no reason to declare war on North Korea. NK stepped out of the nuclear-proliferation treaty long ago, so what they're doing right now is not against any international law. As a sovereign nation, they have every right to develop nuclear weapons. Sure, they're testing weapons in international waters and they trash talk every now and then but so is the US.
I say just let it be. It's not like North Korea is developing a Tsar bomb or anything. Plus it is just so damn unlikely they will ever use those weapons. They would be killing themselves with it and they know it. The way it is, North Korea is making sure with the use of nuclear weapons that no outer force will invade the country. And that isn't necessarily a bad thing. China is happy, Russia is happy, there is no world war with a billion or more deaths. Let's just keep it that way, ok?
Sure, North Korea doesn't have democracy, people are suffering there and everything. But it isn't the goddamn job of the US to bring peace with the use of heavy weapons to every nation in the world. North Korea will have to work that one out for itself, be it by a civil war or whatever. It's just no business to the US. Plain and simple. If they want to help, organize ways for people to escape the country or something. Just don't do it by bombing the country to the middle ages. I know the US really likes doing that, but it didn't work in Vietnam, it didn't work in Iraq, it didn't work in Afghanistan and it sure as hell won't work in North Korea. So just don't do it.
Lastly, if North Korea should really be so stupid to use a nuke at one point, the world can still strike back. In such a scenario, North Korea would be all alone and the war would be over within days. Even if that would lead to an insane tragedy and possibly the complete destruction of Seoul, it would still have way way less victims than shooting first.