I thought that might be the slant-breech model, with rounded action sides. Pretty cool!
The chamber area that the bullet fits into, is usually tapered. The proper bullet moulds were made by Lyman up until about 50 years ago, or at least were listed.
I had one of the Italian versions of the Model 59, bought a .54 hollow based Lyman Minie mould. I cut off the hollow base plug square to the base, and tapered the bullets using a 6.5x68 fl sizer die - rod poked down from the top pushed them out. I had to adjust the die to get the bullet tapered & sized correctly. A bit of fiddling around with adjustments and worked.
These fit the chamber of the replica well, quite perfectly. That rifle had a large chamber area with a tapered bullet seat just like the originals. The Shiloh Sharps replicas made in Montana had a straight chamber, not at all correct. The Italian version held 110gr. 2F GOEX. With the 400gr. bullet I was using, it worked well on a mule deer buck I had called in. I don't think I would shoot a buffalo with it, but about any NA game would cecum to it's slugs.
I didn't use ctg., but would drop in a bullet. I had a short starter in my pocket the correct length to just push the lubed bullet into the throat, then with a horn, filled the chamber with powder, then closed the breech, capped and fired.
The trouble with ctg.s, paper or otherwise, is burning paper bits left in the breech.
My late buddy Brad had one of the Shiloh versions and tried nitrated paper ctgs. After a shot, he would shove a finger into the breech and pull out the scorched and partially burned ctg. paper tube.