The coaster brake is all in the hub. There is the arm that bolts to the chain stay, by the rear wheel. The brake itself is inside of the left side of the hub. You can run a coaster brake on your 73 schwinn, but you need to make sure that the cruiser's wheel will fit properly in the collegiate. I'm not up on schwinns, but that'll be your biggest obstacle, as well as making sure that your coasterbrake hub is the right over-locknut dimension for the other frame, and vice-versa.

Many ppl might advise against this swap, fyi.
Good luck.
-rob