There are two issues with which you are going to have to deal if you do not want to repaint the entire frame. First is color match. To test match, I would touch up a spot that is in an inconspicuous part of the frame, let it dry, and see how it looks. If the match is good, then you might be able to get away without painting the entire frame. Second issue with which you will have to deal is texture. More specifically, when you touch up with paint, the touched-up surface will be slightly irregular relative to the factory paint on the frame. The best way to make this irregularity less noticeable is to use a very fine brush and use that very fine brush to apply a small amount of paint so that it almost "fills" the scratch. Think of patching a hole or gouge in a wall with spackle. That's what you would be doing with paint. Finally, there are products from the automotive realm (Langka? Google search it, its should come up as a touch-up paint) that will allow you to smooth out the surface of the painted-in scratch so it is less noticeable.
All of this is appropriate only if the frame is not extensively scratched. If it is, refinishing is the best way to go from an appearance perspective. However, if teh frame is in good shape aside from a few noticeable scratches and you want to address those scratches, then this method could produce a satisfactory, albeit not perfect, result. HTH. Good luck.
