LED to mount securely in little space (< 5mm)?
I'd suggest a surface mount LED and some glue. They are available in sizes from almost-to-small-to-see up to huge-enough-to-be-used-for-a-car-brake-light. Also available in any color you want. Here are some smaller varieties:



You might attach small wires directly to the LED, or attach the LED to a small PCB and attach wires in turn to that. Or, you might make a one-off PCB with some copper-clad board and a razor blade. Depends on where you want the wires, and what your production methods are, I suppose.

Another possibility is to mount the LED behind the panel, and bring the light through the panel with a hole or a lightpipe. See this page from the Mouser catalog for some ideas.



There are also square LEDs that will fit in that space nicely, which could be mounted simply by cutting the right sized hole. Then either glue it in place, or stick some perfboard on the backside of your panel, and solder the LED to that to hold it in place. If you must have a replaceable LED, you could probably find a way to mount a header behind the panel, and shove the LED leads into it, and friction will be enough to retain the LED if you don't have extreme vibration.