Can an Air Cooler Work Without Water?

Check the manual. If the model allows dry operation, use its fan-only setting; do not run a pump or cooling pad dry unless the manufacturer says that is safe.

Not through evaporation. A unit may still circulate air as a fan, but that is airflow rather than evaporative cooling.

A powered portable cooler needs electricity for its fan and usually its pump. Passive shade and ventilation need no appliance, but they are not active cooling devices.

Evaporative operation adds moisture to the air. If you need cooling without that effect, compare a fan for air movement or a refrigeration-based air conditioner for heat removal.