I tried doing this on an old Continental many years ago, and it was a failure. If you know the frame configuration of a Schwinn Continental, it's a straight shot along the top tube to just under the saddle from the right lever. No extreme bends at all, but yet, it was really hard to get the rear brake to work, even after gallons of Tri-Flow. YMMV, but I doubt it. get a length of inner sleeve housing, re-cut the housing and grab a new cable just in case you get a frayed end.