Swamp coolers do not recirculate air. They need windows cracked to work most efficiently. They also need water. Think of a fan blowing air through a wet towel. Higher humidity kills efficiency.
Maybe you mean A/C? I would suggest rooftop for that
Yeah, swamp coolers need dry air and cool by evaporation adding moisture to the air. You would definitely need to mount it outside the vehicle and bring air into the vehicle and it would need to be someplace very dry to be at all effective. You would also need a water supply like a garden hose or use your own supply of water which seems inefficient. I have been in small buildings in the desert that use swamp coolers and I was not impressed with their performance.
I do mean a swamp cooler, and i do understand their limitations in humid environments. I don't have the weight or power budgets to carry or run a heat pump when i'm off grid, but if i can carry an evaporative unit that is compact and lightweight (and cheap) and can run off 12v solar / battery for a short while to cool the camper down for sleeping in the right conditions then it might be better than nothing.
There are car coolers on the market that can run on 12v , and even more portable units that run off USB/internal batteries. I could just get one of those to try, and they inherently recirculate the air. Or i could make something from a couple of cheap 12v computer fans and a small aquarium pump to circulate air past/through an evaporative pad, and make a frame/housing/ducting that can clip into the opening of a top hung window, sealing around the rest of the window, that can pull fresh air in. Either way, the roof vent/fan would be running to extract warm humid air at the same time.
I did a very quick test last summer with a spare PC fan running under a wire basket supporting a wet mop head draped over it, and I measured a temperature drop from 31c to 24c in the airstream - this was near the Spanish coast in the mid afternoon - not a particularly humid day but not a dry desert environment either
I plan to try filtering grey water from the shower to flush the cassette toilet (self contained) which could also be used for the swamp cooler, so i'm getting two bites at much of the water i can carry. As long as filters and tanks are easily rinsed of any residue when i have access to a hosepipe hopefully there won't be much smell from reusing the water like this.
So, to clarify the original question, as my only practical option is a swamp cooler, is it better to recirculate air that may already have been cooled but that my have higher humidity, or use fresh air at ambient temperature?