The fragility of the razor's edge is more related to its low bevel angle that its width dimension which may be .3 to .5 microns or something like that

The Tennessee toothpick was said to have one side w/ fine sharp edge the other more obtuse, for different uses. The japanese sword too saw different uses sometimes used against Jpn armor, foreign armor, or unarmored duels. There are some differences in cross sectional geometry from era to era, so do doubt there were different edges and final edge dimensions. Most likely they were as sharp as they could be for a given use.

If you are using a polish plane or similar finished-surface woodworking tool the solution for a chipped edge is typically to resharpen at a higher angle not to make it less sharp. Those edges are often just as fine dimension wise as the razor .5 micrometers of there'bouts. I dont see why a "katana" could not be as well; the best hope -a sword meant for unarmored dueling fresh from a highly skilled polisher, working on a very well made blade

Nevertheless a straight razor is typically as sharp as steel can get