how does H2O2 work

ok, so after watching the Mythbusters launch the "civil war era" hybrid rocket, i wanted to make a very mini model rocket that works myself. after some research it became quite apparent that although the fuel part of a hybird rocket (paraffin) is easy to find (PS idk yet if the common grade found in the market is able to sustain combustion but i will look into that a bit after solving the oxidizer issue) getting your hands on a liquid or gas oxidizer in such small quantities is quite difficult, not to mention hard to handle (hard compress oxidizers enough to hold it in liquid form).

after finding about hydrogen peroxide i decided to try and see how it works. i bought some H2O2 from my pharmacy, and obviously, with it being 3% H2O2 and 97% water and stabilizer, it wasn't really going to work. so started purifying it through freezing (will get a little less than 50% H2O2 at best, since interestingly, at 50% H2O2 + 50% H2O, the mixture's freezing point drops extremely and its hard to freeze it). what i'm wondering is, how will >50% h2o2 work as an oxidizer? especially since 50% of it will be water. and also, how does H2O2 (concentrations of like 80%+ that are used for rockets) work to oxidize a fuel in general and how does it work in rockets. also, do other liquid/gas oxidizers work in the same manner?

Thanks for your time