Since you have livestock in your tank, keep your skimmer running.
When I set up a new tank, however, I never put livestock in it until it is fully cycled. I like to fill my tank with liverock and let the dieoff from the liverock fuel the initial cycle. I do not use a skimmer because it takes out some of the stuff before it can turn into ammonium and nitrite. My philosophy is that you want as much ammonium and nitrite as possible in the tank during the initial cycle to fuel the growth of the beneficial bacteria. Letting the tank sit for a month like that (I usuall leave my lights off too), when I come back to it there is an abundance of the beneficial bacteria in the tank. Usually, when I measure my levels at that time, they are all zero. Then I do a big water change and proceed to put in cleanup crew, fish, and then corals in that order.