I have one of those too. The lift mechanism uses a chain, not a cable. Here's a pic of mine and if you look close you can see that it's a chain.
Considering the weight of the machine, close to 30 pounds and then add the section it sits in and you're lifting over 40 pounds. I doubt that a nylon or cord would hold or even work. You might could fabricate an actual braided cable for it, but I wouldn't use anything less.
Joe