I had horrible cyano. I took several steps to rid my tank of it, and so far, it has worked..
I mixed (3) 5gl buckets of fresh SW and removed all the LR from my tank (thankfully it is only a 42gl tank. Next I tweezed, dunked, rinsed, removed by hand and finally gently brushed off with a baby tooth brush all cyano from my rocks and held in clean SW while I took to the rest of the tank.
I scrubbed down all walls. Removed all equipment and cleaned with white vinegar.
Removed the top 1/2 inch of substrate and disturbed the rest so my skimmer would start picking up floating matter.
Then I did a 25% water change before I put everything back in, including blue legged crabs and a cleaner shrimp.
Next I did a complete and total black out for 3 days...ZERO light.
Afterwards I gradually began increasing my light exposure by a cple hrs every few days with another 10% water change after a week.
I know it seems drastic, but I was able to do this without introducing any chemicals to my tank. Its been over a month and there is zero sign of cyano in my tank.
I realize this may not work for everyone, especially if you have an elaborate scape....but it worked for me
Good luck!