It depends a lot on the reason for the touch up.I use various grit,wet or dry sandpaper,these days and the amount of dullness or possible presence of edge nicks,after a shot,dictate which grit.If you are talking about just stropping to remove a burr,that's a little different.I strop on cardboard mostly.
The suggestion of using 1000 grit sandpaper is a good one.I use the KME mostly but occasionally I just freehand the edge with a translucent Arkansas stone that is 1/2"x1/2"x6".That puts a nice polish on the edge of broadheads that have been in the quiver for awhile.