How can I replace Lane pull wire with one the does not break?

My husband is ready to throw out our Lane “reclining” cuddle chair because the pull wire continually breaks. Lots of replacement pull wires are sold on the Internet so there must be a big cash cow in Lane building a break-easy wire pull on these chairs. This chair cost hundreds of dollars and is beautiful. But my husband got sick of replacing the wire so it no longer reclines. They sell stouter wires at the local hardware store but I can’t see how to attach it. Please, help fight built-in furniture flaws. Somebody invent a do-it-yourself wire pull that does not break easily.