I've never used it on any hair algaes, but it does work wonders on cyanobacteria (blue-green algae). Suggestion is to slowly introduce it into the tank, just a little bit at a time with frequent water changes and instead of dumping it into the water column, use an eyedropper to kind of "paint" it onto the algae, this is your best way of using it without killing the fish. It'll take you quite a while, especially if you've got a bad case of algae...
Easier, safer and more effective method might be Seachems Flourish Excel, has worked wonders on hair algaes for me, and if you use paint it onto the algae like you would with H2O2 it should do an even better job... it's gonna take alot more Excel to kill your fish, but still be patient and don't overdo it.