I find laser etching to be a somewhat generic term in many cases (it has been said to mean: evaporation of material (both to leave a mark and remove "dirt"), melting (and reforming) and addition of material/dye just off the top of my head).
This being said a fair few plastics (which courtesy of the hinge thing probably includes the DS, this includes thermoset and thermoplastic types) do not take kindly to being heated like this.
I am not much of a laser engineer (laser welding is about I really did in depth, marking is a whole other thing really and I only really scratched the surface of the area*) but assuming you are going to evaporating material I suggest going to a fast repeated scan/trace to a roughened surface with a properly calibrated laser (power, wavelength and such I would not really feel comfortable suggesting without doing some calculations).
Edit:* I can assure you that was no pun.