I used a pumice stone and some lexol leather cleaner. It might have looked nicer if I used sandpaper, as the pumice stone left some scratches, but the strop works fine.
I've had mixed results with restoring vintage Russian Shell strops. The tanning process and finish is something kind of like the surface of fine grit barber hones: when you abrade the surfaces, they just don't look the same ever again.
I've had good results with sandpaper as well, I've never gone to high grits, but regular sandpaper up to 400 grit gives a nice velvet finish to strop surfaces. Sometimes it takes quite a few sheets of sandpaper since the paper loads pretty quickly and take some time.
On new leather for making your own strops, sandpaper up to 400 grit works just beautifully, IME.
I used a pumice stone on a latigo strop and finished with some micromesh I had laying around... finished at a very high grit (10-12k) and the area became almost horsehide-like. I'm actually very tempted to do it to the whole strop.