Ann,
I don't see anything wrong with putting the shifters you want on the Schwinn.
That said, I've kept the old SunTour barcons from my '72 or '73 Nishiki when I sold the frame, and they've got black handles. They're now on my '92 Bridgestone RB-2--I took the newer Ultegras off that bike and replaced them with the SunTours.
So if you've got black-handled SunTour barcons, they're probably just the thing for your '73 Schwinn if that's what came on the originally.
Unless, of course, you just prefer the downtube shifters. . . .
Nath Dresser
Spring Green, WI