Yes, Like Dave says, Use a brass or nylon bore brush. And yes, like Car Nut says use a rust inhibitor, Shooter's Choice is good.
There are many good rust preventitives on the market. Many are the same thing just packaged different. Walmart's wonderlube is Rem
Oil, etc. I like G96 the best as it cleans lubes & protects. Do not soak the wood with any
oil or rust inhibitor, also do not apply it so heavy for it to run into the wood & soak it. Just a light coat wiped on the metal parts after removing the rust. An old trick & the cheapest is to use automatic tranny fluid. It does wonders & leaves the metal looking nice. Many dealers use it at gun shows to have their guns looking their best at sale time.
Rat, Cleaning of antique firearms is not taboo as in the case of cleaning antique furniture, etc. But it must be done correctly. Just like cleaning your Cobra must be done correctly. A wire wheel on your aluminum kirkham body for cleaning is just as wrong as on your antique firearm.
Bronze wool & light
oil rubbed gently to remove rust & grime is the way to go on firearms. This removes the active rust but leaves the overall metal patina.
The bore of the firearm- you can get aggreesive with but not so aggressive as to scratch it. After removing what you can with a brass or nylon brush with solvent, I then go to a product called lead away. It is a yellow cheese cloth that can be cut into squares. I then take a square of it & place it over the bore brush. I use a plastic gommet (purchased at a gun shop) to protect the breach or muzzle end (I prefer to go in from the muzzle for this procedure) & use a rod that can be hooked to a drill. Spinning the brush with the lead away cloth will remove lead & grime like you never thought possible in the bore. It will remove all the crap which you thought was the bore surface & leave it clean as a whistle with out scratching the bore. Using a grommet to protect the muzzle end is a must as the lead away cloth will also remove the finish & any patina from around the muzzle exterior where it comes in contact with while inserting & removing it. The cloth with come out pitch black for so many times you won't believe it! If this procedure intimidates you, you can have the lead removed electronically by any good gunsmith. Or just leave the bore alone as only someone wishing to shoot it will care about bore condition. This is one of my favorite cartridges & I reload them. Brass is now available but years ago when it wasn't, I used to form it from 348 Winchester brass. It worked good but 50-70 brass extracts better & will last a lifetime. If you have any questions at all, best to ask before you do something. You have a great piece of Americana that is rich in history. The last book I authored titled "Guns That Talk" is a collection of photographs & captions on firearms with unique histories. The title came from the old saying "If only it could Talk!".
Regards,