Generally speaking, rather than asking how to *kill off* the string algae, the question is...why is it there in the first place? ALWAYS better [safer + more economical] to determine the CAUSE of an an issue & address that than it is to treat symptoms.

The stream is about 1 ft to 2 ft wide and about 200 ft to 300 ft long. He as put some small dam in the steam maybe about a 1 ft or so deep. It flows into Cayuga Lake one of the Finger Lakes in New York State. The lake is about 2 miles wide and 40 miles long.

I do not think there is anything that to do other to manually pull the alge.

Here's a good doc that goes over some treatments.

My experience with drug store type hydrogen peroxide.

There are different chemicals used to control string algae. All have basically the same issue. They're all perfectly safe and say so over and over. When you read the MSDS (Material Safety Data Sheet), the only place sellers are required to tell the truth, you'll see an entirely different story. These products are only safe when applied exactly right. Apply a bit too much and you kill fish. And that's how sellers define "safe", fish don't die within a few hours of application. It's like saying it's perfectly safe for humans to breathe carbon monoxide, as long as you don't breathe too much.

Of these chemicals the ones containing hydrogen peroxide (HP) are safer imo, but can still kill fish if over dosed. These use HP in granular form, many times stronger than drug store HP and millions of times stronger than the few molecules of HP produced by rotting organic material like barley straw. Strong HP kills string algae almost on contact.

Question is then what's worst, a pond/stream full of green string algae or brown string algae? IMO it's easier to remove live string algae than dead. Certainly a massive amount of decaying string algae can cause water quality issues, but much less so in a natural stream which is always being flushed. Either way it has to be removed by hand. Kind of defeats the purpose of the chemical. However, once string algae is removed HP can be used weekly, or a few times a week, to keep killing new growth.

Because this is a natural stream whatever chemical you add would be flushed away. That makes chemical much safer for fish. But it also means you'd have to apply more often. For HP treatment I'd guess you be talking about hundreds of dollars per year.