Faust,
I am very cautious when I give advises. People new to Nihonto with no track records must absolutely follow the most conservative way, i.e. oil +shirasaya, add store bag on top. Will it damage the shirasaya, not if the blade is thinly coated with oil. Furthermore, for the excess of oil, shirasaya have a small reservoir at its bottom.
NOW, the shirasaya must be made of honoki and in pristine condition because THE SHIRASAYA must be AIRTIGHT, beware of old shirasaya, they have to be checked and clean by a professional.
Now concerning my experience, I never had rust on my non oiled blades kept in Shirasaya. They were on a katana kake and thus I could study them at length whenever I wanted without having to wipe them, reoil them, I am the lazy type but I know the subject by heart and don’t take unnecessary risks.
For beginners, adopt Darcy B. policy, oil them, don’t take any risk because Art and money are at stake.