first of all I'm assuming you took TN screen out already, otherwise do so now, since when I was replacing my screen I was very confused: the MB connector was on left, and cable went inside right hinge so I thought screen connector was on the right, but new screen had connector on the left. Only after taking old screen out I realized original screen also had connector on the left and the cable was run long way around.
Also, on my computer, with little tinkering you could run cable through either hinge, maybe you could run your cable on the other side also, making the distance shorter and therefore being able to use original cable. You can buy cable all by itself, but the problem is the only cable that is 100 % guaranteed to work would be direct replacement for your computer and that one you already know is short. Buying longer cable for different computer may work, but as already some mentioned, connectors especially on MB may be different.
Possible to get longer 30-pin edp cable?