Unfortunately you must treat ALL of your fish or treatment will be ineffective. With most diseases, once a pathogen is in your tank, all susceptible animals must be treated. The general treatment for black ich is repeated (over a period of days/weeks) freshwater dips and/or formalin baths, however you really should move your fish to a hospital tank. This allows you to leave the DT free of all potential hosts while the remaining worms starve out. I have been told that the tank should be left fallow for 12 weeks with this parasite.
If you absolutely cannot set up a proper treatment tank, you *might* be able to eradicate the parasite through regular dips of ALL fish. However, there are disease that cannot be treated in the DT so you will find a hospital tank necessary, particularly if you don't quarantine.
Black ich is caused by turbellarians, which unlike ich, are capable of surviving in the substrate on detritus, for a while, without a host. The do require a host to complete their life cycle. The black spots seen in this disease are the actual worms, which are capable of moving freely about the host. From what I understand there are some invertebrates, like sea cucumbers, that can also host these worms.
Regular marine ich is caused by Cryptocaryon irritans, a ciliate protozoan, that parasitizes fish exclusively. This parasite produces small, round, white nodules on the fish which give the classic 'sprinkled with salt' appearance. The white spots are actually cysts produced by the fish's skin in response to the irritation caused by the parasite. This is why freshwater dips are not very helpful for this disease, the fish's skin protects the parasite. Treatment relies on killing the free swimming forms of this parasite.