At what level dosing Hydrogen peroxide to a reef tank that would kill cyano and not kill chaeto could be tricky not to mention the effect it would have on other organisms in your tank you are not aware of. Hydrogen peroxide is a very strong oxidizer that is a sterilant at high enough levels.
From Wiki:
"Hydrogen peroxide (H2O2) is the simplest peroxide (a compound with an oxygen-oxygen single bond). It is also a strong oxidizer. Hydrogen peroxide is a clear liquid, slightly more viscous than water. In dilute solution, it appears colorless. Due to its oxidizing properties, hydrogen peroxide is often used as a bleach or cleaning agent. The oxidizing capacity of hydrogen peroxide is so strong that it is considered a highly reactive oxygen species. Hydrogen peroxide is therefore used as a propellant in rocketry.[1] Organisms also naturally produce hydrogen peroxide as a by-product of oxidative metabolism. Consequently, nearly all living things (specifically, all obligate and facultative aerobes) possess enzymes known as catalase peroxidases, which harmlessly and catalytically decompose low concentrations of hydrogen peroxide to water and oxygen."
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What does this mean, well since organisms can render harmless small levels of hydrogen peroxide, then at these levels hydrogen peroxide will not do much. The trick would be to use it at concentrations above what the organisms can handle and below the level where it kills them or damages cells leading to disease possibly. This can be different with different coral & other inhabitants like algae and macro-algae and there can be a difference among different species of algae as well & the same with different species of cyano which is documented in research. Lighting and other factors can play into the equation as well.
You are simply guessing at this level without any true facts to back it. You don't know the specie of cyanobacteria you are dealing with. Hit or miss so to speak and can cause serious damages to tank occupants if you are wrong. Keep in mind if you play with fire you can get burnt.
I think if one were to add household bleach to a reef tank, most hobbyists would open there eyes a bit, yet sodium hydroxide is a stronger oxidizer than household liquid bleach by a good shot.
Just my two cents.
