If you like the unstained walnut color, you can try 200 Wet-or-Dry paper to rub in a bit of finish, then wipe the slurry off as it fills the grain, wait a day, re-apply as needed. Finish with same process with a few applications of 400 or 600. Leaves a deep, matt finish.
Tried this process with a stained stock but, despite my best efforts to be careful, some sharp edges & corners had stain sanded out. Putting a dipped finger-load of finish on the paper, then hand-rubbing in a small area is key as the finish will tend to get sticky afer a minute or two.
The slurry from the sanding & finish, then wipped away, fills the grain in walnut. This takes me at least 5 applications but leaves a tough and lovely finish that seems resistant to scratches and wear.