Just did two radiator deletes. I tried two ways to blow the air out and they both worked. The key is to get the air out of the high (back) end.
Option 1 -- If you have a tilt trailer or a way to get the front end significantly higher than the back end (large snow bank). Get the front end up. Run the engine for 1-3 minutes. Stop. Let cool. Fill the cooling bottle. Repeat the process (run, cool, fill) until you do not need to fill anymore.
Option 2 -- if you do not have a way to get the front end higher. This may sound stupid but it works. I have done it twice. It is based on taking advantage of the fact that without the front radiator the cooling system is completely circular and that fact that in a closed system air can push a liquid. So here goes. Remove the plastic pieces that cover the cooling hoses near the back radiator. You might have to remove the rear rack. Remove the metal clip that holds the hose onto the back radiator. Do not take off the hose. Start with the hose on the right side. Only remove the clip that is closest to the radiator. Loosen the hose from the metal. You should be able to twist it to make it loose. You are trying to make room for air to come out under pressure. Once the hose is loose, blow a deep breath (it will take several) into overflow hose on the cooling bottle. Keep blowing until you get coolant flowing out of the hose where you loosened the connection. Once you get coolant to flow put the metal clip/clamp back on. At this point you will have all the air out from the cooling bottle to the radiator. Now we want to get the air out of the radiator...if there is any left. So remove the same clip from the other side and repeat the process. Depending on how much coolant you need to get in you may have to fill the cooling bottle every now and then. There should always be coolant in the bottle. If it becomes too hard to blow into the overflow hose open the cooling bottle and let air out. That is the air that will be the air you pushed through the system. You will probably hear a gurgling sound as the coolant replaces the air in the hose. Remember it is a continuous circuit so the gurgling is because the air is being pushed out of the circuit. Once all that is done you may have a little air left and that should come out next time you run the engine. With mine once I ran the engine the coolant went from the fill line to about where the connection to the throttle body is.
You could probably do the above with compressed air just make sure the pressure is not too high as to pop a hole in the rubber or any other place. Remember it is a closed system and the air will have to come out somewhere.
Good luck.