Can I slow an air cooler's fan speed with an additional regulator?
After looking at the photo and the units size I am guessing it is a evaporative cooler commonly called a swamp cooler as the water falling down with air flow creates cool air. If this is the case you could slow the fan but remember the cooling is based on the air flow.
If I am wrong and the cooler uses a refrigerant you should not adjust the fan as slowing the fan can cause the system to ice up. Icing affects system performance and in severe cases can damage the evaporator coils.