In case anyone didn't catch it, the redneck in the video was going through an exercise to make *rule 2* look stupid.
Dana,
If you still want to use gas at this point, you should be able to get a tank of CO2 from your local welding supply / compressed gas shop. You'll also be able to rent a regulator and probably buy some hose. While the potential to freeze the bird definitely exists, I doubt the Joule Thompson cooling would be sufficient to lower the temperature in the chamber more than a few degrees unless you open the valve wide open.
If you want to displace oxygen in the bird's system, industrial grade nitrous oxide may be available from the compressed gas shop and would probably be about as humane as you can get. It may take a little longer but would certainly do the trick once the oxygen is displaced completely. Its my understanding that the nitrous oxide displaces oxygen on the blood's hemoglobin molecules and causes one to lose consciousness due to oxygen deprivation - the same effect as holding your breath until you pass out. This made me reconsider what kind of anesthesia to get at the dentist.
-DB