This is a longshot but if it works out, it'll be an excellent way to get your hands on exactly what you need. Get in touch with a company who makes or repairs windows in your area. There is a part called a spiral tube window balance that is basically a metal tube with a spiral twisted piece of metal inside. If you can find a place that has just the tubes, no guts inside (most likely either a window parts manufacturer or metal recyclers), you're in business.
If that doesn't work, try copper pipe or electrical conduit pipe from a local plumbing/electrical supply store. If HD/Lowes don't have them, try the places the local contractors use like Locke Supply. 1/4" Copper is too small, 3/8" is probably too big, but if you can find some 5/16", that might work for you.