I have used wet-dry sandpaper on a couple pieces of linen. I have never needed to go lower than 800 grit and finish on 1500 to restore the appearance it came with (which I like). Loaded stropps are fine too, but they generally will result in a polished not-so-micro bevel that is visible...and over time will turn the tip into a compound bevel. Nothing wrong with that, but if you like the way it was originally and want to maintain it, I would not use the strop much.
In summary, treat the tip like a zero grind convex with a 1500 finish.