That's one good carving knife.
Farrier's hoof knives (single edge) and all the crooked carving knives (double edged) here in the Pacific Northwest are "in-cannel,"
that is, the single bevel is on the top, the inside of the sweep curve. The underside is usually hollowground a little.
For edge management, pipe is the way to go.
I use several pieces of thin-walled 3/4" aluminum tubing.
The abrasives (800 grit, 1500 grit & CrOx/AlOx on office filing card)
are wrapped around the tubes and secured with no more than masking tape.