>If the laser is green, by the time it's flying away at 0.2c, the laser won't be green any more thanks to the Doppler effect! I'm too lazy to calculate, but it will definitely shift toward the red.

Interestingly, you also have to deal with Lorenz contraction - at .2c the ship itself will shorten by about half a percent, compounding the apparent wavelength shift. Admittedly this is a much smaller effect.