You scenario is a false dichotomy. You have to realize 1) Air Force One is considered a Sensitive Compartmented Information Facility (SCIF), so any sensitive documents that a President may need while traveling can travel with him; including having classified information sent to the plane. Beyond that, anytime a President travels, there is almost always a SCIF set up in the local area that they can get the President to quickly.
I'm not taking about Congressional oversight anyway. I'm saying that Congress should pass a set of laws that set up the rules and requirements that everyone must follow (to include Presidents and Congressional members). The President could still declassify information, though it would be good to have laws in place that require a minimum set or rules covering declassification -- such as some type of notification system to show that document is no longer classified (though that system might itself be classified). While you do have the issue that the President (through his DoJ) would be responsible for enforcing the laws he is to follow, OTOH, Congress does have the power to impeach if the President does not enforce those laws.
Edit: I ran across
this article which talks about the government has turned shipping containers (the type used to transport goods on container ships and trains) into SCIFs, which allows the SCIF to simply be moved to the location the President is traveling, rather than having to find a building they can turn into a SCIF (sound proofing walls, securing, etc) for a few days.