Thanks for your responses. Ironically, you'd probably be better off with a flintlock weapon than a cartridge or percussion cap weapon. From my own research (British Muzzle Loaders - a wonderful Youtube channel run by a Canadian chap who has thoroughly researched the drill, life and weapons of imperial soldiers from about 1800 to 1900 has been extremely valuable) you can chart the development of firearms as machine tools and metallurgy advanced in the 19th C
The biggest challenge in making any fire arm is going to be machine tooling and the quality of the steel going into the stressed parts, never mind the precision required. The technological leap from the Brown Bess style military musket (the main infantry weapon of British forces from 1740 through to 1815 (dates are my own guestimate) and the Baker rifle that Sharpe uses in the books and on the telly is a considerable one primarily because of the tolerances demanded by the rifle and the quality of the barrel,
Today you can buy a kit to build a Baker rifle from a company in Canada. The only thing not included is a barrel - for this you need to go to a gunsmith as it is the barrel that requires the specialist engineering bit and because you don't want to kill yourself with an exploding breech.
I think a good starting point over the 'cobbling together' of weapons could be the Afghan jezzail, the often home made rifle made by the tribesmen of 19th C Afghanistan. These were usually built by local craftsmen and the firing locks found are a mix of matchlock and flintlock, percussion locks start to make an appearance. Early on the firearms are almost all matchlocks, a matchlock is a relatively straightforward thing to make, a tinsmith might be able to cobble together a crude one. Flintlocks in these weapons have machined parts and require a spring - again a sophisticated bit of metal, needing high carbon spring steel - making such by hand is a specialist job as any watchmaker will tell you. The reason why we start to see such in many Afghan made weapons in the mid to late 19th C is due to recycling flintlocks from British and Russian made weapons. However, the more skilled artisans would have been able to make the locks and springs but I suspect that in most, springs were recycled from captured or salvaged British weaponry.
The wheel lock is a sophisticated and complex design requiring again, sophisticated metallurgical skills and and understanding of clock work. If drum springs could be found then there is no reason why a crude matchlock couldn't be made. As to the primer issue - this is the biggie and this is the thing that really rules out cartridge weapons, black powder or otherwise or percussion caps - never mind the skills required to produce machinery to make the actual caps themselves. So I reckon that in reality, any cartridge weapon of 20th or 21st C design is going to be obsolete in a post apocalyptic 2230 because of the primer isssue. Gunpowder is also an issue - sulphur being the major headache.
Throughout the gunpowder age in Europe, the primary source of sulphur were the sulphur mines on Sicily in the vicinity of Mount Etna. Saltpeter and carbon can be extracted from local sources (local = Scottish Highlands and islands in the setting of this book) but sulphur is an issue. Now, such would require relatively sophisticated and extensive pan European trade routes however, 200 years after a population destroying non nuclear apocalypse As to gunpowder quality - IF the effort of building a firearm as described above is deemed worth it then there is no reason not to think that such would not exist. I am a trained archaeologist and there's ample evidence of fine axe heads from what we now know as Wales, being traded as far a field as modern Russia during the neolithic period. Flint mines in southern England supplied quality flints across Europe for a period of 50,000 years or so and the discovery of a stone age sea going trading boat on the south coast of England indicates that such trade routes were commonplace for desirable or essential materials like quality flint.
Corned gunpowder would not be beyond the skills of someone who knew their history, it merely requires adding water to the blended gunpowder, forming it into cakes before crushing it and sorting the larger corns from the finer ones using a sieve to get your different grades of powder (priming powder vs charge vs cannon charge vs explosive) corned powder is a much better prospect than uncorned especially for those who need to travel.
Sten guns with black powder? I suspect they would probably jam due to fouling of the barrel after a magazine worth - one of the reasons why gatlings etc used multiple barrels - also is the pressure from black powder enough to drive the bolt? I wouldn't know.
So looking at all the above, a more feasible projectile weapon would probably be the crossbow. Which is, after all, a 13-14th C in its final widespread military use. Tests have shown that a hand cranked crossbowman can lose around 8 bolts a minute when working at top speed (about half that of a semi competent longbow archer) Yes crossbows require some skills to make but are not beyond an artisan. They are easier to use than longbows and do not require the years of dedicated practice longbows require
composite bows again, are not beyond a skilled artisan. Horn and suitable wood can be laminated together with a glue made from boiling fish air bladders. They might, however, suffer in the damp climate of Scotland.