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Most coticules auto-slurry. After 60 roundtrips (my edge refreshing routine) the water on the coticule always is a bit "muddy". In the olden days coticules were never sold with rubbing stones. Only...

Going back to the opening post: why not use sandpaper? Gives nicely rounded smooth edges on your stones.

@Tristan: interesting study on coticule and BBW you discussed. As your link didn't work when I tried it I copy-pasted it here:
file:///C:/Users/User/Downloads/BBW-study%20(3).pdf

I did not know...