Black Trochus snails eat it and I have used them in the past, however you need a whole lot. Those are the best snails in my opinion period, and the only ones I have ever seen eat cyano. Liveaquaria has the best price/best specimens. I've ordered them from other places with high death toll but generally all make it from liveaquaria. You would still need to syphon the cyano from the sand bed as the snails won't go there for it. I would keep up with syphoning it manually as much as possible anyhow. If you use a smaller (like 3/8") hose you can syphon it out great without sucking out a ton of water.
If you can afford, or can't have the snails due to fish predators, then I would suggest chemiclean. Follow directions to the T, and do not overdose the product. I have a mixed reef with acros, monti, basically every sps you can think of, many different lps, zoas, etc and I had no issues with any of my coral. In fact the day after many corals looked better than ever. I had very little cyano at that time, but it was enough to cause annoyance.
If you do some searching, chemiclean is actually a highly suggested dip treatment for zoas with issues. I also have used it for that purpose with good success. I save some colonies that were having issues sporadically for a long time, and they are doing well to this day.