That is a fascinating idea -- if i did it though I would want to follow a strict recipe. If I had a standard bottle of 3% Hydrogen Peroxide you can get at the drug store, how much of that would you add per gallon of saltwater, and then how long would you let it sit?
If i had a 5 gallon bucket with chaeto in it id probably add 100 ml of 3% grocery store peroxide and let it sit for 12 hours. If no change to the hair alge id add another 100ml and wait 12 hours. Youll find your sweet spot to kill it. Iirc algae barn washes their algae in peroxide. @AlgaeBarn