Just take apart the whole tank and clean it all at once, rocks and sand. Best way of all.
While apart, swish rocks around in separate bucket of clean saltwater so the cyano, and the detritus pent up in the rocks, is cast out
Rocks are cleaned in saltwater only
The sand is taken out, rinsed in tap water until it's totally cloudless, then in saltwate to clear out the tap. Rinsed 110% clean in freshwater so you have enough, then in salt as final prep.
At no time reassemble a cloudy new tank. Be so thorough in cleaning that the rocks and sand are cloudless cleaned and the new system will be balanced, invader free and laser clear. Under rinsing the sand is top risk. Rinse in tap until it's snow globe clean.
Full new water, set all this back up it doesn't recycle. Acclimate fish back in, corals don't need acclimation. I have a video of me doing this to my 13 yr nano after invading it on purpose with cyano, just to show a cure run. It's the above steps exactly.
Any other method or doser leaves sandbed waste in place, plus dead mass from treated cyano. This method is safest and best option for nano reef control for sure.