Do mystery snails carry ich?

I’ve got an ich outbreak in my large African cichlid tank which also contains a bunch of large mystery snails. I’ve treated the tank with copper and malachite green but I’ve just read that this can be toxic to snails. I could move them out of this tank, but my only other tanks are a quarantine tank containing new (healthy) fish, and a smaller tank with about 30 peacock fry. Would moving the snails into one of the other tanks risk spreading the ich? I definitely don’t want to risk killing off all my fry. Should I just see how the snails go with the malachite green and copper?