I think the best solution would be for somebody to make a few varieties of hollow joystick shafts w/ some different shapes and colors of translucent handles. I may work on this myself sometime (way too long from now for anybody to get hopes up) I don't think it would be that hard to throw some tubing on my dad's lathe and machine the appropriate grooves for a few joystick styles. I have some omni-sticks, wico-microswitchs, and 1 wico-leaf I could try to make custom shafts for. I know I can get clear balls from a plastics company locally that I could frost, drill and tap.
More on-topic for what you are asking... if you cut a custom shape out of plexi, sanded it, and lit it from the sides so you only get indirect light through it then it wouldn't be like looking at an led through a window, you would have a glowing plastic part, you would get a similar, but less defined effect w/o sanding it, but the frost may make it more apparent.
Another Idea would be to take some fiber-optic strands, maybe from a silly lamp (should be some at a thrift store) or novelty flashlight (carnival, or theme park,) and drill tiny little holes in whatever shape you want or maybe little holes all around your joystick in a circle, put the fibers in and run them all to an LED somewhere under the CP.