The lack of a protective atmosphere would probably leave it far more exposed to radiation if kept on the surface or in a container that isn't lead-lined or the like, which would probably degrade the paper...

But this is getting more convoluted and more than my limited knowledge and understanding can provide for - your best bet might be to reach out to Randall Monroe of XKCD.

Heck, it's the kind of question that belongs in his book: "What If?" https://www.amazon.com/What-Scientific-Hypothetical-Questions-International/dp/0544456866