I use a good quality cherry oil stone which I bought years and years ago ... man, I'm getting old
It's a decent size block measuring 8" x 2" x 1" which is good for restoring these stems 'n' stuff
Like most stones available this one has two grades ... coarse and fine
TIPS
Place the oil stone on a good flat surface or secure it in a vice or workbench ... work the item you're restoring back and forth on the stone making sure you keep it flat at all times. Keep the stone well lubed at all times too
I prefer to remove any anodising before using the stone ... all chrome will have to be properly stripped before hand too
Steve