Keith,
There is nothing wrong with using air to purge the cooler, however that does not purge the torque converter also like the method that I recommended. Blowing out the cooler with air only and not purging the torque converter will probably take an extra 1 to 2 quarts of fluid as apposed to the 2 gallons that I mentioned, because most of that was going into the converter.
There are three types of transmission coolers used on Beaver coaches. There is a air to oil standalone cooler in front of the radiator that is seldom used because it will not help in raising the transmission fluid temperature in cold weather to keep the transmission at the proper operating temperature. The other two designs are both coolant to oil coolers. One uses a cooler in the radiator end tank, and the other design uses a cooler built into the radiator inlet hose. The one that is built into the radiator inlet hose is preferred on 4000 series transmissions because they help the transmission reach operating temperature quicker, and the 4000 does not do as well cold as a 3000. So you see that a transmission cooler is also used as a warmer when necessary. The main goal is to keep the transmission at the proper temperature at all times, not too hot or too cold.
Gerald