Hmmm. The tip of one of my screwdrivers is still embedded in my thumb after the eye-fixing incident. I actually ended up wedging a bit of hard plastic into the eye for a couple of games (which worked surprisingly well) before taking it down to SP to have it fixed properly.
If you are going to solder it, the one word of advice is to tin the ends first, and use a HOT iron on the pins for as short a time as possible, or else the ribbon just melts.
The eye is nowhere near as small as surface-mount chips are, so it's do-able even with a "normal" chisel-ended electronics soldering iron.