In my experience, line depth isn’t as important as line spacing. Scrimshaw is nothing more than crosshatching ( like is done with pen and ink) except it is cut in first, and then inked. The differences in the line spacing, are what give you the shading, that creates the three dimensional effect.
I do a lot of my scrimshaw with a large screwdriver type handle made by Exacto, and one of their hook billed blades, that allow you to make cuts without dragging the back end of the blade through the work.
Hungry Horse