The cable housing shouldn't be a problem if you have the standard Schwinn metal ferrules. You can always wrap a bit of tape around the cable end to make it fit tight in the ferrule.

Where your shifters are mounted -- won't that interfere with the brake cable routing? Isn't there a cable stop right there for the brake cable?

If the shifter clamp goes around the top tube, it might also work around the handlebar stem. I'd be tempted to do a stem mounted setup. It would look more original and you wouldn't have to worry about them sliding around -- although I doubt that would be an issue wherever you put them.

I did a indexed conversion on a Le Tour using thumb shifters mounted on a set of MTB handlebars. Worked great and lets me shift without having to move my hands.