I understand why you want to (re-)line the barrel so you can shoot it. The thing is, you may have a rare piece that was issued as a fowling piece. Unfortunately, although I looked at 35mm film Records of Arms and Ammunition in the Hands of the Troops, I don't recall any mention of such a piece being issued. At the time, however, I wasn't looking for the record of such a piece. It might take me awhile to go back and recheck the records, as I don't have a film reader, and will have to take time to go to the library with the films. It may be a month before I can get to it. Could you wait that long before modifying the carbine?
As to the mechanism under the hammer, that is what is left of the Lawrence pellet primer action. If you were to remove the hammer, you would see a cam groove on the inboard side of the hammer. Before conversion to cartridge (or shotshell), these were percussion-fired arms. Note the open slot in the right side of the lockplate. A number of fulminate of mercury pellets were loaded into the vertical reservoir in the top of the mechanism. (The large round-head screw was removed to open the top of the reservoir. A number of the pellets were dropped (carefully) into the opening, and the top replaced. A sliding piece with a projection on the right side that fit into the cam slot on the side of the hammer. When the trigger was pulled, the hammer flew forward, and the sliding piece was cammed forward, stripping a single primer from the stack. It flew forward just in time to be hit by the nose of the hammer, setting it off, and the resulting flame passed through a passage in the original breechblock, setting off the paper or skin cartridge! When the piece was converted to metallic cartridge, there was no need for such an arrangement, and part was removed and the nose of the hammer ground off flat. A new breechblock with an oddly-shaped firing pin was installed in the receiver. The nose of the hammer was ground off flat to hit the firing pin extension.
Another interesting thing about the Sharps conversions: When the Army issued the M1873 Trapdoor Springfield's, they recalled most, but not all the Sharps Carbines. A small number of the Sharps Carbines were retained by cavalry units in the field. These were used for target practice and so that the troops could use them to forage for game, as only 3-5 rounds of .45-70 or .45-55 ammo were allotted per man per month for target practice! There were, however, about 50,000 rounds of .50-70 ammo at Sidney Barracks, NE, alone! The Sharps were also issued to scouts and other civilian employees of the Quartermaster Dept. who accompanied the troops in the field. Co. G., 3rd Cavalry retained 5 of these Sharps when issued their Springfield Carbines, and brought them to Sidney from Ft. D.A. Russell in 1874. According to records extant, they still had them at Sidney when the Ordnance records stopped in June 1876. I researched this unit thoroughly, but do NOT recall any indication that any of the five were smoothbore. At least one utilized by a young civilian teamster was definitely rifled. Hope this is of some help and interest.