You don't need a skimmer, but I would highly recommend it... just for example, with your tank fully stocked as is, you would probably need to be doing about 3 times the water changes you would have to with a skimmer, in order to keep water quality in line. Over time, the decrease in money spent in salt will definitely pay for itself. Basically what a skimmer does is remove organics before it can be broken down into nitrate and/or algae, both of which are not so good.
But, onto another issue... are these canisters the only form of water movement you have? And, what make and model are these filters (well, what I really want to know is how much water there pushing)? With a low water flow rate in your tank, detritus tends to build up, cyano bacteria (type of nuisance algae) does much better... your water quality suffers.
Also, you should know that you definitely want to quarantine these fish, the reason being that they are sometimes described as "ich magnets"... not only that but they are not that resilient to this disease, meaning the few treatments you can use in a display most likely won't work fast enough to save the fish.
AND, learn what lateral line erosion is... this is another ailment (not really a parasite, just a dietary deficiency) that tangs are susceptible to... The way you prevent this is to learn the proper diets for these fish, then feed them said diet.