To the best of my knowledge, strops are relatively new (last three or four centuries, anyway). Swords were generally sharpened first with a grindstone, then with finer and finer stones. The smart thing to do would be to bevel the edge a bit so the cutting edge was sharp, but not that sharp. The edge might be tested with something like a piece of straw, but the idea that the straw (or whatever) would actually slice itself by its own weight was a graphically impressive, but unrealistic bit of fiction.

All this assumes broadswords rather than the later rapier or the much later smallsword. A sharp edge on a broadsword was not that important, because fights with broadswords generally involved the defensive shield and/or armor. Fighting with a broadswords was more often like fighting with baseball bats. Most rapiers (circa The Three Musketeers or Cyrano de Bergerac) had cutting edges, but they were primarily thrusting weapons. The smallsword (the light, slender sword worn by gentlemen in the late eighteenth and early nineteenth centuries didn't have a cutting edge. Strictly thrusting weapon (no matter what Hollywood duels look like).

I'm not just guessing about this. This comes from my life-long interest in fencing and some books on period arms and armor.

Don Firth