Only the President can decide what happens to his records and documents. This has been made clear under Navy v. Egan. Congress can pass no laws regarding classification or record keeping. The Presidential Records Act has a caveat where the "personal records" of the President belong exclusively to him, and it's the President who decides what is personal or not.
That's a fascinating interpretation of PRA, which establishes public ownership of all Presidential records. Specifying if a record is private is the responsibility of his/her staff and done at the time of filing. Of course, Trump has tried to quote from the PRA, but he's not charged with any PRA violations, but under the Espionage Act.
