Refinishing, rust removal, etc of an antique firearm is something to be started only after prayerful deliberation and with the concurrence of a burning bush. You run the risk of devaluing the piece.
That said, to remove the rust and any leading from inside the barrel, mechanical means such as JB bore paste on a cleaning patch (probably lots of cleaning patches) might work, or electronic means - you can build a low voltage electronic bore cleaner that should remove the crud via electrolysis. Plug the cylinder end of the barrel, fill barrel with a vinegar/ammonia mixture, suspend a stainless steel rod from the muzzle end taking care it doesn't touch the barrel, put 3-6 volts DC across it (positive to the barrel, negative to the suspended rod), and give it 20 minutes or so. Dump the cruddy mixture, then clean the barrel well and oil.
Again, whether you are better off taking such action with an antique is something for you to decide.
Good luck, SCL