I am hearing that you are used to working with freshwater tanks and you are confused about the air stones being needed or not.
Saltwater does not like the airstone air bubbles in the tank. I can actually hard corals and other critters in the water. The power heads will give enough flow through the tank to allow for proper gas exchange. I would completely remove the air stones and hoses from your tank.
The skimmer air pumps will actually help to remove bad stuff from the water. It will not have any effect on the gas exchange from my understanding.
I hope this helps!!!