Hi Wahoo.
There are correct expensive tools for doing the job but unless you know how to use them it can all go disastrously extremely fast. But all is not lost!
There is one method I would recommend that is as old a gun manufacture itself the Lead bore lap. It is simple in its manufacture and use. Firstly plug the bore tightly with a damp rag just below the place where the choke is reasonably smooth and acceptable next top the rag with a damp card disk the size of the barrel at that place. Next pour in molten led making a lead plug the same size of the choke and try to make it as long as practicable, as it cools the lead shrinks making it easy to knock out of the bore with a cleaning rod and a perfect size for the bore.
Because the barrels where cold you will find that the sides of the lead will have random groove lines and that is what we want in this case to hold the abrasive compound. Just for completeness if we wanted a lap with smooth sides we would need to heat the barrels but if the gun is vintage the barrels could be soft soldered so be careful you dont re melt the jointing solder at the muzzle. Drill a hole lengthways through the lead lap and mount it on a piece of threaded rod sometimes known as studding bar using a nut and washer at each end, cut the rod to a length that will encompass the choke length plus enough for holding in a drill chuck.
Use fine grinding paste and cover the lap ease it fully into the bore (if you dont do this there is a high chance you will end up with a bell mouth) use a slow drill speed and keep the lap moving while you polish.
Now the reason why this form of polishing lap is reasonably safe for polishing a bore is as the abrasive particles embed themselves into the Leads surface they will polish the bore but at the same time they also wear the Lead so making the lap self limiting to the point it will stop working and you will have to cast another.
Yes Lead and its fumes are toxic but so is aspirin and Lead/Tin Solder unfortunately we are not going to live for ever so it's pays your money and takes your chance.
