Use Tru-oil. It's worked for gun stocks for decades. The finish is also very easy to touch up. Tru-oil is a tung oil base, with additives to speed drying time.
Sand the wood to 400 grit. Then, take a damp (not soaking) towel and wipe the surface of the wood, and allow to dry. When you sand, some wood fibers are just pushed over, not cut. When the damp wood dries, those fibers will stand up. It's referred to as "raising the grain."
With the first coat of Tru-oil, you'll want to apply it with 0000 steel wool, or wet-dry sandpaper. You don't want to soak the wood with the oil. Just put a few drops on the surface, then sand lightly with the steel wool or sandpaper to spread it around. As you sand, you spread the oil around the surface of the wood, and also sand all the fibers that you just raised. You'll effectively create a slurry of fine sawdust and oil. As you sand, you'll be shoving that slurry into any open pores in the wood, thus filling the grain.
Once you have a light coat over all the wood (you don't want any runs), then hang the knife to dry for 24 hours.
On the next coat, card the first coat with 0000 steel wool, dry. This abrades the surface of the Tru-oil so that the next coat will adhere. You can apply the next, and subsequent coats, by hand, rubbing the wood hard so that you can feel the friction in your palm.
Card with steel wool, apply a thin coat of Tru-oil, hang to dry for a day, and repeat.
With 2-3 coats you will acheive a satin finish. Ten coats or more and you'll start to get a high gloss. Some high end shotguns could have 30 or more coats.
Once you have put on several layers of oil you can also finish with a paste wax, but that may not be necessary if you've acheived the look you want with just the Tru-oil.
If the handle ever gets nicks, scratches, etc., just touch it up with a little Tru-oil and let it dry.
A bottle of Tru-oil will cost under $5. If you only ever use it for knife handles, one bottle will last a long, long time. If you use it infrequently, place a piece of plastic wrap over the bottle opening before putting on the cap, otherwise the oil will dry out.