Any penetrating oil finish will work but there are considerations. Depth of protection will depend on species of wood and density. So if you remove .250” then all bets are off. Most oil finishes penetrate at most in domestic low resin hardwoods about 1/16” . High resin species and highly figured domestics woods tend to absorb less. I would suggest a 40-60 or 50-50 mix or tung oil and real turps heated to around 120° or ballpark close. Tung oil and oils like linseed response well to moderate heat and viscosity reduction allowing better penetration. Tru-Oil and similar products contain quite a bit of driers or metallic salts which provides the user with a great looking and handling topical finish but reduced penetration

Good luck

at most I will need to remove .030" where the wood is proud of one side of the upper tang and the same for one side of scallop to the receiver. And just want to see if doing that work after a few initial coats can be easily matched. I am not staining the wood and it is American Walnut that needs some filler for small porosities.

Matching surface finishes with oils is not a problem. You’re not staining so color match is basically irrelevant. Clear oils work essentially the same and only change tone with age and UV exposure.  Shellac’s are high build low penetrating fast drying barrier coats that really don’t do much for gunstock work other than tone and fast surface build. Using a shellac is strictly the ultimate topical coating with little to no penetration. Shellac is one of the ultimate base or barrier coats but this is not what you need.

I'd give it a coat of Minn Wax Wipe On Poly. It is very thin, and will soak into the wood quickly. Might even give it a few coats, as raw wood sucks up thin finishes. 
But I usually keep a box of nitrile gloves on the bench and wear them when working new wood. Easy to keep oils from my hands off the wood, and stuff off my hands too.

Polyurethane coatings offer the user a couple of features. (1) ease of application which Minwax was built on, (2) fast dry and short recoat windows, and (3) good tough abrasion resistant hide or surface. What Polyurthane does not offer is UV protection. No inhibitors or filters so poly gets brittle with age and sunlight/UV exposure and begins to yellow. Unlike oils poly needs to be stripped to restore or at best sanded back and recoated before it yellows.

Poly is really not a penetrating oil like Tung, linseed, etc. that never fully hardens. Penetrating or drying oils actually create a molecular bond with wood fibers while polyurethane is a surface coating. Some oils can darken with long exposure to sunlight especially linseed however Tung oil doesn’t appear to. Polyurethane is a polymer or plastic coating and like all plastics it will break down after a while and must be stripped. My comments are specific to single part common polys like Minwax etc however there are two part catalytic urethanes that offer much greater flexibility, gloss retention and UV inhibitors. However these are costly, difficult to apply in many respects, and contain very toxic isocyanates. Not a product for your average hobbyist. Oils like tung and some others are very very water resistant and can be rejuvenated for many lifetimes. Take your pick.

Wouldn’t a light final sanding over the entire stock take care of any oil staining from handling with your hands? Or just wear lightweight gloves when handling it, that’s what I would do.

The depth of a hand rubbed oil finish is like no other and I can clearly tell if something other than has been used.