If the filtering of broad spectrum light by the button to pass what appears as green is not too narrow a filtering, it could be allowing little or no red, very little orange, just a bit of yellow, most of the green band, a bit of blue, and very little or no violet/ultraviolet. So if one were to put a bright enough “pure blue” LED light source behind the button, 80% of that blue might not make it through, but what did make it through would be seen as blue. In a darkened room, then you’ll see a blue button. If the room has a decent amount of light in it, however, there will be enough green reflectance from the face of the button to ruin the ‘blue illusion.’

Another option that would be some work, but less than molding a new button, would be to obtain a 5, 8 or 10mm diameter blue LED. If you can ‘flex wire’ the LED, then drill a hole in the button that will allow the LED to fit in the button snugly and travel with the button when pressed. If you will attach the LED in a stationary manner, drill a hole in the button that will allow the LED to protrude a bit but is just large enough to allow the button to be depressed and released easily, using the rim of the button that is around the LED while the LED itself does not move. With light misty coats, paint the button black or blue before combining the button with the LED and switch again. The LED will require only a very small fraction of the rated current to be bright when in view so be sure to be generous with the value of the series resistor. If the LED is not diffuse enough, you might need to alter the surface.

If all that is too much trouble, paint the button black and remove its light source and add a status LED nearby. Or provide a switch somewhere out of view and just turn the button location into a status light.