H2O2 is produced by the cells of the body as an immune response to infection and for production of energy in the "fight or flight" syndrome. I don't believe that extra intake of nascent oxgen in the form of H2O2 (Hydrogen-Peroxid) will hinder this process. It may even enhance it. You're right. In high doses, H2O2 (Hydrogen-Peroxid) in water tastes nasty. That is because of the tin and other stabilizers in it that keep the oxygen from out-gassing from the liquid too quickly.
An ozonator is an electrical device that changes oxygen (02) into ozone (O3). You can read about ozone and types of generators at