On the titled question of, "Can Trump Just Declare Nuclear Secrets Unclassified?" Lawfare's Alex Wellerstein, a historian of nuclear weapons, answers at prior length:
One of the difficulties with all of these issues is that there is essentially no precedent in applying them to the president. Some precedent exists for presidents trying to make certain things secret at will, or for the government trying to censor the publication of secrets, but really none when it comes to presidents asserting that they have declassified something secret and thus cannot be charged for mishandling it. It just hasn’t ever been an issue before that I can see. That means that it’s difficult to predict how the courts would rule on it, because on top of the First Amendment issues, you are also getting into deep questions about the power of the president—a nebulous area when talking about national security issues. Though, again, usually the issue has gone in the other direction—presidents expanding secrecy, not reducing it....
One interesting consequence, though, of Trump’s current defense is that if he did truly declassify these documents, then they ought to be obtainable, at least in part, under the Freedom of Information Act. Are Trump, his lawyers, and his defenders suggesting that these documents should be publishable?...
It does lead to the complicated question of "graymail" though: if Trump were to be prosecuted for these documents, and did claim that he had declassified them, and was successful in this claim, would this not mean the documents were truly declassified and thus could be compelled to release? Depending on the sensitivity of the documents, would that be enough to convince the government to avoid prosecution by itself? Without knowing more about the contents of the documents, this is all very idle speculation, but they do raise a lot of genuinely thorny and genuinely novel legal problems.
Only Trump could have created such bizarre entanglements — the most interesting of which is the possibility of nuclear weapons' top secrets being subject to the Freedom of Information Act.
The first person to submit a request? Kim Jong-un.