Mainly get moisture when warm air hits cold parts, in this case its cold air hitting hot parts. I duct a 5000 btu window unit right into my cards and have no problem "other than my electric bill".
What's a 5000 btu window?
I guess it's an aircon.
However I believe that cooling air with an evaporative air cooler is much more energy efficient.
Or a combination if you care for comfort.
I'm not sure about the energy efficient aspect at all - I did consider an air conditioner. My rigs will be pulling around 4.8kwh total. A conditioner would add 3.5kw per hour!

EDIT: Maybe after reading there again I've misinterpreted you. I assumed an evaporative air cooler was the same as a conditioner - never heard of them b4.
What about just venting the heat straight outside? Then at least you're not trying to cool the heat that's being produced. I guess air is going to be coming into the house from somewhere with that kind of venting?
If you had all 4 rigs next to a window that had a few beefy exhaust fans I assume that would at least get rid of the heat. Unsure how that would effect the rest of the basement though.