Schwinn "Chicago" first used the plastic end caps. They were a "clear-whitest" color. Even back then when they were new and still pliable, they were very tight to put on. You quickly learned NOT to use your fingers, but to use a needle nose pliers. One experience of driving a brake cable up under your fingernail is usually all "the learning" it required for a new employee.
They were replaced by the aluminum "crimp-on" caps. These were a big improvement, easier to install and stayed in place. In Arizona, the plastic caps often dried out, cracked and fell off. For some reason, I remember the aluminum caps were considered expensive, like a nickel per cap or something crazy. We would always make sure to not lose the new caps in the parts bags and pick up any on the floor. Weird the things that stick in your head.
These were the only safety caps I remember Schwinn-Chicago using. They used Weinmann and Dia-Compe caliper brakes almost exclusively. Kelsey Hayes built the Krate disk brakes and Campagnolo was used on some of the Paramount's. Campy had a really cool metal cable cap with a set screw.
I think the other cap (with a ball) your thinking about likely came from other vendors (that built imported bikes for Schwinn).
John