Ah, finally I found somebody else who sings the lyrics the way I sing 'em. Also, this site (click) seems to indicate that in 1935, the Junior Birdmen of America was an official program of the United States Bureau of Air Commerce.
Note the name of the tune - takes us one step closer to finding it. Click for the original "Army Team". "Junior Bridmen" is a simplified version of the chorus of this West Point fight song.
Click here for a great choral recording of "Army Team."
-Joe Offer-

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Junior Birdmen
[Tune: On Brave Old Army Team]

Up in the air, Junior Birdmen; up in the air, upside down,
Up in the air, Junior Birdmen; with your noses to the ground.
And when you hear the grand announcement: that your wings are made of tin.
Well, then you know, Junior Birdmen, it's time to send your box tops in.

For it takes: 5 box tops, 4 bottle bottoms, 3 coupons, 2 wrappers, and one thin dime!

Actions:
Make a face mask each time you sing the words, "Junior Birdmen" by lacing your fingers. Then, with thumbs under the chin, twist your hands outwards so that you make goggles for the eyes.
On "Upside down,"perform a jet plane swoop outstretched arms.
On "Ground," bring the swooping arms as near to the ground as possible.

Source: http://home.twcny.rr.com/uncleted/onondaga/program/songs.pdf