For the stock, you could give it a little sprucing up with some Johnson's paste wax on 0000 steel wool. You're not looking to bear down on the steel wool, just give the stock a light buff-down and remove haze and surface gunk.
As for the steel, if the blueing is in good shape, then all you need to do is wipe it down with a light coat of oil. An old gun in good shape that doesn't have damage or rust is entitled to have a patina of age.
Refinishing: Worst possible of all worlds is someone buffs out the metal on a wheel. Corners get rounded, details are lost, lettering is washed out. Real refinishing means real work, polishing by hand with polishing paper backed with a hard object. I have a bunch of aluminum and walnut blocks I used for backing paper into tight spaces and corners and use a bunch of different types of papers to get the finish right. I'll polish up to 400 to get rid of 320-level marks, then I might back down to some used 320 paper after the 400. Polishing that preserves details and is hard to detect takes time and some skill.