I'm not terribly good on the individual derailleur model names before the late 60's (hell, back in the early 1960's, I didn't even realize that Schwinn made anything but the balloon tyred middleweights - then again, I wasn't even a teenager at that time), but I'm certain that Schwinn used some version of the Simplex pull-chain derailleur on the rear. I'd start seriously looking for one. From what I understand, they aren't the greatest shifters in the world (Campagnolo's Gran Sport was miles ahead of the competition at that time), but I've seen them for sale, and while not cheap they aren't prohibitively expensive.

You've got something rare enough there that going back to original would be almost mandatory. And I'd love to see what it looks like after a disassembly, gentle cleaning and polish, and reassembly. That's the kind of bike you want to take to shows!