The only time that I noticed moisture
in the air from a swamp cooler is if it was a portable (indoor) model. They continually recirculate the same air over and over adding more water to the air. That or when people have the outdoor rooftop or side vent going and don't have windows slightly opened to allow the hot air to be pushed out. It's a science but easy to do. Most evap coolers can replace all the air in your house in under five minutes, usually less. Some people think you have to close up every thing as you would with ac, but the opposite is true. I don't have ducting, all air comes in at one place,the cooler vent. The test they use goes like this: You open one window in every room, just a little,say 2-3 inches . Then go to the furthest room from the cooler, and hold a piece of bathroom tissue about a foot from the open window and release the tissue. If it falls to the floor, you need to either open that window wider or reduce the openings in other rooms. This is if you need more cooling in the further reaching rooms. You have to experiment with different window settings in the house to suit your comfort needs. The air will take the easiest path. P.S. If that tissue paper flies and sticks to the window screen the same way in every room, then you've achieved a good balance. Hope that made sense.