I wouldn't recommend the freshwater dip for a fungus/white cotton problem on zoanthids. The freshwater is primaraly for trying to kill the nudibranchs. Thats why I mention the hydrogen peroxide dip.
About 3-4 years ago when the barbie pink zoanthids started hitting the boards, alot of them came in and developed a white cotton/fungus starting at one end of the colony and spread to the other end, fairly fast. Usually to other colonies of different colors, with nearly 100% death.
On Reef Central the 10% hp with 90% tank water was one of the tools used.
I used this dip with all pink colonies when they came in and were still healthy.
I never got that fungus thing, when other people that received frags from the same place did get the fungus, that didn't dip.
I also read about people using a tetracyline dip. Some swore by it.
So, like I said do some searching on RC and read the info that people posted and be your own judge.