It sounds very logical to me, that laboratories used much larger stones than barbers and such.
This is because of several things.

In laboratories for the past centuries straight razors or devices with equivalent cutting edges have been used in what is called microtomy.
Here a sample that is to be examined under extreme maginifaction is sliced into extremely thin slices.
This way cellular structures can be seen.

It is important to have an extremely clean cut because of two things:

first: "scratches" on the surface of the cut left from teeth or burr on the edge will become visible under high magnification and will lead to detoriation of the microscopy

second: the slices have to be extremely thin (literature speaks of single digit micron thicknes) to prevent multy-layers. You want to look at one layer of cellular structure only.


Devices used for microtomy can consist of a straight razor, or much larger microtomes. These are devices that will automatically cut thin slices with a very large knife, seen here:


Such big knives need big stones, I guess.
A coticule, as well as an arkansas (perferably black, I heard) and BBW were used frequently