A clicking sound can come - as far as I've experienced - from 2 different causes. Often it does not pose any further problem than the sound itself, hence the first thing you need to do is find out if it imposes damage upon the edge. As been said, magnification and a good light source are required to rule out this possibilities.
1. a foreign inclusion is embedded into the surface of the Coticule.
Examine the sturface with a non-precious razor, while make short strokes. You need to pin point the exact location of the inclusion. Circle the area with a pencil, and look for the inclusion. Use of magnification may be in order here. The inclusion can be pried out. This is explained in the
Coticule Repair Faq, chapter 4.
2. a small crack runs transversal across the surface.
Some Coticules have very faint manganese lines in the surface. It rarely happens that such a line is not a line but a small crack. In such instance, the crack sometimes changes direction deeper into the stone, and starts running parallel with the surface. If this happens the surface area above that crack will be ever so slightly compressible. It will likely escape attention that while lapping such a stone, the cracked part compresses with each lapping stroke, only to spring back. This result in a minimal, yet abrupt level change at the crack. The razor will notably "click" when it bumps into the higher part.
If this is the case, you need to locate the crack. Fold a piece of high grit sand paper 2 times over, so you get a thicker fold of sand paper and use that fold to lightly sand the crack down. You only need to bring it a couple of microns below the rest of the surface. The clicking sound will be gone, and so will be any possible damage it could do.
For a more permanent solution, an attempt to fixate the Coticule must be made. This is described in Chapter 3 of the aforementioned FAQ-article. Once the cracks are fixated with glue, the surface is no longer compressible and one final lapping will cure the problem.
Kind regards,
Bart.