The cold steel greatsword doesn't come with a sheath or scabbard so, would it be prone to rust/corrosion or not? And if so, is there anyway I can prevent it from doing so?
Actually having a scabbard does not automatically prevent rust - it does prevent dust from landing on the blade and soaking up whatever oil is used to coat it.
Best product to use for a naked blade is called "Renaissance Wax" which is what they use in Museums. It coats the blade in such a way that dust will not actually touch the blade.