I did this same thing awhile back. You can get the really small lamps for the buttons from Radio Shack. I got the display backlight lamps from a local electronics store.
For de-soldering, you can buy a de-soldering iron with integrated squeeze bulb from Radio Shack. There is no need to 'mask off' the area as it'* already covered by a green conformal coating on areas that aren't supposed to get solder (pc boards go through a wave soldering bath).
For soldering, use a 27 to 33 watt iron on pc boards. Heat the solder pad with the iron and touch the solder to the opposite side of the pad. When the solder melts and flows, it will form a nice mound around the component lead. Remove the iron at that point.
And BTW, you don't need to completely remove that instrument cluster bezel. Just remove the two retainers above the steering column, snap the area around the radio loose. It will swing out far enough to reach in and release the four tabs and pull the radio out. Only connector I had to undo was the DIC select/reset switch panel because it doesn't have enough slack to get the trim piece far enough out on the right side for radio removal.