Idk if this will work on the 93 but in my ng you take the radio out my inserting the radio removal tool in the little slots on the corners and it comes right out... If you dont have that tool you can also beng some hangers to shape thatll work as well...
There's a bunch of ways to get the headunit out, I stick the non business end of four drill bits into the holes and pull it out, I've read others who have fashioned a "removal tool" from a wire coat hanger.
It's just a matter of getting something in the holes to "unlock" the clips.... piece of cake.
Not sure what you'll do after that, I've never tried to clean the laser on a disc player.