Get a burnisher, as in a flat one like a very fine file. Should be about ÂŁ40 for a decent one.
Get a lollipop stick and sandwich the pivot between the stick and the burnisher using for example your left thumb and forefinger. Then you can spin the wheel by hand using your right hand, whilst using your thumb on top of the lollipop stick to roll it along the burnisher as you turn it, applying a very light pressure. Don't let the pivot spin against the burnisher in one position, you need to keep it moving across the surface of the tool. You are trying to remove any damage whilst keeping the pivot straight. Very important not to get it tapered.
Easier to do than to explain!
I have a Jacot tool, but still use this method if I only have one or two to do. Works well on biggish clock pivots, once you get down to watch sizes you need the proper tools.
You also need a decent loupe so you can see the results.
If you only need to do it occasionally then you could get a piece of flat steel and glue a strip of 2500 grit or finer wet and dry to it in lieu of the burnisher.
Ideally they should be polished afterwards as well.