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I can offer two suggestions:

1) I would regard going from a coticule with water to a barber hone as a step backward. Even with lather, even if it's a Swaty 3 line or a Perfect brand hone.
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I have not found this to be the case (chrome ox used on edges that have previously been honed on stones/hones rather than pastes degrading sooner than hones with no chrome ox).

When the edges DO...

Short answer, yes. You'll like the edge improvement/refinement off of most any hone/stone.

Chris L