Since BMX basically got started with modified StingRays, BMX bikes adopted the Schwinn standard for headset sizing. So yes any 'old school' BMX headset should fit, with one caveat. BMX bikes and post '65 Schwinns used a 21.1mm stem, pre '65 Schwinns used a 7/8" (22.2mm) stem. As a result the hole in the top nut of a BMX headset may be too small for the stem on your Traveler. You may have to reuse the original Schwinn locknut or open up the hole in the new nut a little bit.

Rhenning's suggestion to use loose balls is a good one if the cups and cones are still in decent condition. But if not, any of the better BMX headsets would be a reasonable substitute for an original Schwinn. Hatta, Tange, and Tioga all made some very nice BMX headsets that were easily the equal of (if not substantially better than) the Schwinn parts. Unfortunately NOS vintage BMX parts can be quite spendy these days and would probably be more expensive than NOS Schwinn parts.