It would be an experiment with obvious risks (right??), but IMO worth a shot. It's not a lot of peroxide and the peroxide isn't really that strong if that helps.
I think I'd consider taking a sample and running some tests for dino's.....see if you can shake up a sample really well and knock all the brown off of one of the strands. Take the "clean" strand out. If you then leave it sitting in the light, the dino's ought to re-group into a little mass. Other things like cyano or diatoms won't do that. You can also add some peroxide to the vial (maybe use another tank sample that you don't shake up) and see if you get a lot of bubbling – that's a sign of cyanobacteria.
You might want to peek at this to see if your current conditions seem favorable to dinoflagellates:
Dinoflagellates – Are You Tired Of Battling Altogether?