I would say DO NOT try to sand it by hand. You will end up with a more rounded pin than you started (and you'll nick the CG all over the place).
I don't have anything fancy like a lathe, but I get decent results doing the following: Push out pin and carefully place in the chuck of an electric drill (you'll need a decent one with no wobble). Then I run the drill very lightly against a very flat surface with sandpaper on it (a plate of glass or tile works well) being super careful to keep it at 90 degrees (if I had a drill press I would be using that). I start at 600 grit, then to 1200. By then it's should be looking pretty flat and shiny with a very square edge. You could probably stop there, but since I have them, I move to 3M abrasive films all the way down to 0.3 micron. At that point, if I've been steady and careful, it looks like a mirror, flat and spotless, even under my 20x microscope.