Hydrogen peroxide will destroy a watermaker membrane as quickly as bleach, and the carbon filter won't stop it. If used, make sure it is either flushed completely, or has sat around long enough (a month or more) to decompose.
2% hydrogen peroxide is useless in sanitation of the tank. It needs to be far higher than this to do that job. Commonly available hydrogen peroxide is 3-5%, so 2% of that is ~0.08% - a meaningless concentration for sanitation.
H2O2 is available in 15% bleaching solutions, and 90% industrial applications, but this isn't easy to find and requires careful handling. It would be somewhat impractical for sanitizing compared to cheap and easy bleach.
I've heard of using HO as a method of killing bacteria in water supplies, but suspect it's not by adding store bought concentrations. Not going to work with the watermaker in any event. Thank for the ideas anyway.