P.S. Can Occam's razor (or any formal presentation of it) be classified as a hypothesis?

Sadly, no; this is the "problem of induction" and to put it briefly, if you try to do what you suggest you end up having to assume what you're trying to prove. If you start with a "flat" prior in which you consider every possible Universe-history to be equally likely, you can't collect evidence for Occam's razor. The razor has to be built in to your priors. Thus, Solomonoff's lightsaber.