Simply, yes. You will be reducing the compressive strength of the wood by taking away fibers that would make it more resistive.
The integrity loss from engravings could be compensated for by using a slightly thicker piece of wood (the compressive strength then being equal to or greater than the deepest groove – if none were greater than say 1/16", then adding 1/8" to a 1" diameter bo would give you a 1" core.), or by using a more resilient hardwood (using a 3/4" hanbo of osage orange [horse apple], I have broken 1" white oak hanbo on multiple occasions).
Carving with a knife can have additional consequences. Often, if the wood is too dry, the knife can cause further splitting than intended, and your 1mm cuts will become significantly deeper. For this reason, I find a Dremel to be a superior tool for this sort of work.
Any engraving should be followed by a full sanding of the wood, then re-oiling the wood with boiled linseed oil to permeate the newly exposed fibers. This will improve the flexibility of the fibers (their ability to bend without tearing) which increases compressive strength. Please note that only boiled linseed oil should be used for this purpose; regular linseed oil will not permeate the wood effectively.
Very Important! You're using white wax wood, which is a very flexible wood with medium to long fibers. It takes a beating and compresses nicely. Any engraving will shorten exterior fibers, so good sanding and rounding will prevent splintering. Follow with oil to prevent the bigger threat to your engraved wood staff: Wood Worms.
Wood worms burrow into wood, eating away at it which compromises core integrity by creating little tunnels. White wax wood is extremely susceptible to these little pests. Regular oiling and care are a must.