Many people don't use skimmers on zoanthid only tanks.
Some people say that zoanthids like more nutrients in the water and that running a skimmerless tank is better for zoanthids.
I personally don't completely subscribe to that idea, but I don't have a working skimmer on my zoanthid tank at the moment. Only because the pump died and I just haven't had time to do the mods to it before setting it back up.
If you have any fish in this tank or other corals, plan to feed the tank with solid foods, I'd look into a skimmer.
JMO