Getting a skimmer is not going to solve the issue of your overstocking the tank unfortunately. I concur, remove the two blue tangs and you should be fine with whatever skimmer you can get.
I had 3 tangs in my 125g and they did well, but were still needing more room. I had a yellow, blue and bristletooth tang. I waited for a 180g to come along before I go to four tangs and even that is pushing it.
180g Reef - 60g Rimless Reef -90G FOWLR- 125g Malawi Cichlids- 40b REEF- 34g Fresh Planted-working on- 20L FOWLR- working on
I have a mix of many different saltwater fish amongst my tanks, but I love my Tangs most of all.