The use of a single groove "Guideline" checkering file is the best way to do a border. Draw the perimeter on the handle and slowly file it in. They come in left and right cut to allow filing both directions as needed. Deepen as you go around. A regular single groove checkering file will also work. Go slow, several passes around the border is far cleaner looking than one deep cut.
Next, decide if you want holes or bumps as the fill pattern. For holes, use a small carbide ball burr and stipple the surface evenly. Start from the sides, going around the border and slowly filling toward the middle. For bumps, us a cup burr to make little round bumps in the same way as the holes. Hole stippling is easier to learn. Bumps take higher skills.
With holes, you can sand the final patterned area lightly to clean it up. Bumps must be very carefully sanded or the bumps get flat tops. Steel wool is a good finishing material for both methods. After any sanding, brush out well with a stiff bristle brush and burnish with a soft cloth. Staining the background dark, and then buffing hard with a soft cloth to lighten the high spots is a standard finishing method.
Burrs come in fine, medium, and coarse cut. For finish detailing like handle and gun stippling and patterns, use the fine cut. The harder the wood the better the finish cut. Brush off the burrs and keep them clean so they continue to cut clean markings.
I find "engraver marker pens" and other vibrating electric markers leave a horrible pattern on any surface. They are fine to write an ID number or name on a metal or plastic item to prevent theft, but the marks are a jumble of uncontrolled shallow dots. On a handle they would be a terrible choice.
A hammer graver handpiece will work fine on annealed steel and other metals with diamond or carbide, pave' or stylus point, but they just break the grain on wood and make an unattractive pattern of tiny splits and dents. These don't look anything like the ones created by removing wood with rotary tools ( holes and bumps).
So, there will have to be some sort of wood removal to get a good pattern.