Well, cyano can grow with no nitrate and phosphate, so I think you would be best to try to cut down it's nutrients. Use RO water so there is no nutrients in it. Feed less 'til the problem resolves. I am not a fan of using chemicals to kill it, because it does not deal with the root cause. The nutrients will still be there to feed some other nuisance algae.
Do you have a sump where you can grow some good algae to suck up those nutrients?
You can also use a power head to blow it off areas where it is causing trouble, and let it grow where it is not. Then, as the nutrients are used up, it can be sucked out.