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A Coticule with water will surpas a pasted strop everytime, not only will the shaves be nicer, also you won't end up rounding the bevel, meaning the time between full honing will be greater.
I'm quite a beginner and only got my first hone (a coticule) 4 monthes ago so it's maybe a 1 cent advice.
When I use unicot , I never have to rely on crox.
With dilucot when I have a lesser day, I sometimes finish on balsa hone with crox, or when I have a problem in the finishing stage I give the edge 10 strokes on a balsa with crox then finish with X-strokes on water.
So I think it could be useful for a beginner
when you get your stroke and technique under control, you should be able to get excellent results using the coticule alone. I always found that pastes leave my face feeling a bit raw.
I believe the OP was referring to a hanging crox strop?, I have used a balsa one and then gone back to a Coticule, I do not believe it will work with a hanging strop, because of the convex bevel it will create
In the beginning, the edges will benefit from pasted stropping, because they make for easy keenness, while a Coticule demands experience for achieving great keenness. Although the Unicot approach really makes it easy. But Dilucot and other approaches can be challenging. With growing competence, you'll notice that pasted stropping no longer improves the edge. And eventually, you'll reach a stage where pasted stropping makes it worse.