Some thoughts.
1) Sharpie and other ink or paint applications would work but CAN run or spread in the fibrous wood, depending upon the type and porousness.
2) once you have applied the Sharpie, a cover coat of some sealant MIGHT contain a solvent that smears or ruins the picture you just drew, especially if you rub it in.
You need to test it out first. I am thinking..
Also, consider a type of scrimshaw application on the handle ?
Good luck
ChuckC