Why not just use the edge of the coticule in the same manner as one would use a japanese nagura? Rub it like a pencil eraser and you'll get a slurry. The coticule nagura I sell all have flat edges to them and this is how I've used them. Putting coticule stones flat to flat would result in a lot of surface tension and cross hatching is a solution you can use as well. Machinists use a cross hatched steel plate for flattening metal and the cross hatches do double duty. One, they reduce surface tension and two they provide channels for the swarf.

Howard
BTW, I call the belgian nagura "Cotigura" to honor the Japanese tradition but to differentiate as a belgian stone.