If it were my rifle I would wipe it down with Murphy's soap and immediately dry it off. If the finish was good I would use a quality wax on it like Renaissance, Briwax or any that have Carnuba wax in them.
I would be tempted to at least rub it down with Artist grade Linseed Oil thinned with turpentine before waxing. If you wanted more durability then Linspeed or any of the better spar varnishes could be mixed in at half linseed, 1/4 turps, and 1/4 varnish or less.
Regarding Oil and shellac mixes: James V. Howe has a formula in "Modern Gunsmithing" using shellac and linseed oil. Many of the formulas for Slacum used by Purdey and others have shellac added as a filler. LC Smith and Parker both used an oil shellac mixture for finishing and Parker would mix oil, shellac and varnish for really porous wood.
I didn't think it would work until I tried it and they are not only compatible but produced a nice finish faster and with at least initially more water repellent properties than oil alone. Not as durable as any of the modern finishes but traditional.
All good information but where would you put BLO in your points? I am sure you are aware it is the lowest grade of linseed oil with driers and drying inhibitors added which severely affect its value as a quality wood finish...
