something that old might have to build it if you can't find it. without a model and serial number it is hard to find obsolete parts, they may have been superseded. 1993 is 30 years old on a push mower. Maybe look at some Sears Craftsman mowers from that period and see if any match yours. Or build your own, or get a newer mower.
https://www.mcmaster.com/products/bowden-cable/