Let's start with understanding what algae means in your pond. Algae grows when you have excess nutrients in the water - fish waste and left over food are the two main sources, but excess organic material in the pond can add to the nutrient load as well. So rather than thinking of the algae as the problem, think of it as a symptom of a problem. It's like when you have a fever - the fever is uncomfortable, but it's not the main problem. Your body uses a fever to signal that there's a problem And like a fever, algae is often both symptom AND solution - the algae is telling you that you have excess nutrients in your pond while it's also helping to remove it.
The first response is usually to want to rid your pond of algae by killing it. The problem with that approach is dead algae adds - you guessed it - more nutrients to your pond. Kill the algae and all you're doing is feeding more algae. It's a vicious cycle. So rather than trying to kill it, you should aim to control the algae growth by controlling the nutrient levels in your pond.
Three ways to control the nutrient level: fewer fish, less food, more plants. Simple, right? Actually it is that simple - but it does take patience as it will not reduce the algae in your pond overnight. So while you are waiting, the single best "algaecide" for string algae it manual removal. Just get yourself a tool of some sort - a stick, a toilet brush, or even your hands - and start pulling it out. Toss it in your garden or compost pile - it's got good stuff in it!
There truly are no safe or natural algaecides. They are all designed to kill and, even when used correctly, can cause harm to the living organisms in your pond. Unfortunately many people misuse these products which is even more disastrous.
I hope this is helpful. I know it's not the quick fix you were hoping for, but you did express interest in a safe and natural approach. I will also mention that I noticed that you said you power washed your pond. By doing so, you removed one of the most beneficial aspects of your pond - the biofilm that develops on the underwater surfaces is one giant filtration mechanism. Power washing is not recommended if you hope to keep your pond ecosystem alive and functioning. Just thought I would add that as food for thought -