I don't think there has to be a "process" at all. Just some record that it actually happened while he was still President, not just a verbal assertion made only after he is no longer President.
For example, the letter he signed stating that he was declassifying the Crossfire Hurricane documents is completely adequate. Why not just do that for the other stuff? Hell, a simple letter signed and left on the desk while he is still President saying "I'm taking the following documents to my home, and hereby declassify all of them."
The argument that a president can take an action that has legal effect simply by thinking it, and not telling anyone or writing anything down, is ridiculous. As I said, the perfect counter example is Obama claiming years after the fact that he mentally pardoned a bunch of criminals< who therefore must now be released.
"Legal effect"; I think that is a good term to use here.
What are the limits to the authority of Congress to dictate how a President handles national secrets? Could Congress demand that the President inform Congress each and every time a document is classified or declassified? Could Congress legislate that classification lapses automatically after 30 days? Could Congress dictate that the President's State of the Union address is classified and that the President does not have the authority to declassify it.
Help me understand the limits of Congressional action and then I can better explain my position. I maintain that the President is simply not bound by the classification system. It's a tool that he can use to do his job. He is the master not the servant of that tool.
The impeachment of Andrew Johnson illustrates one possible case. Johnson was impeached, in part, for violating the Tenure of Office Act. This act dictated that Johnson needed permission to fire his own cabinet heads. Johnson violated that act.
The law was later modified and eventually repealed.
Of interest is the following statement in Wikipedia: "While evaluating the constitutionality of a similar law in Myers v. United States (1926), the Supreme Court stated that the Tenure of Office Act was likely invalid."
Congress has a recognized role in providing "advice and consent" to the appointment of officers under the President. They have no role in dictating that the President cannot fire them.
Similarly, Congress has no role in dictating what is classified and what is not classified beyond that with which the President agrees.