I have had that same issue with a couple of bikes this summer. The way that I solved this issue is to use a couple of magnets along with some very fine welding material, and coaxed the welding wire into the hole with the magnets. Once the welding wire is through the holes, superglue some fine fishing line to it and pulll it back through. Once the fishing line is through(be careful not to pull it out of the holes) superglue the cable to the fishing line and pull through. It does indeed work, but it definitely needs some patience and persistence!

For future, before you pull out the cable, super glue the fishing line to it and that will solve the problem. Many of the early 90's frames did not have internal cable guides, so don't assume that yours does. This applies to both road and mountain bikes.

Good luck and keep me posted!