Weapon restrictions don't always make sense in the real world using gamer logic. Shotguns are generally more allowable than rifles and pistols not because they do less damage, but because they have more general utility for hunting small game. Some countries put a limit on the ammunition so that you cannot use slugs for example, but buckshot will still kill quite effectively. Pistols are often heavily restricted for their concealability, the US has wildly varying rules about concealed carry and open carry from neighbouring states. Bolt action hunting rifles might be perfectly legal by default (e.g. Germany) but any sort of semi-automatic loading might be illegal (e.g. UK). There are often exemptions that might make sense locally but no sense to an outsider.
In the UK our gun laws have evolved over the last century or so often in response to isolated incidents for political and public opinion reasons completely unconnected with any credible effectiveness of the legislation. Shotgun ownership is still reasonably common as it is a required tool for farmers. Not all shotguns are legally classed as shotguns though e.g. semi-automatic guns capable of holding more than 3 shots, short barrelled guns etc. You can own certain types of pistol if you are a member of a gun club, others are banned outright. You cannot own a self-loading rifle unless it is a "smallbore" (.22 rimfire for example). Using a "full bore" rifle of any kind requires a special license unless you only intend to fire blanks (in the UK the license also covers the purchase of a certain quantity of ammunition), so owning the weapon itself might not require such a restrictive FAC. You can own antique weapons designed for "obsolete ammunition" with no restriction even if you actually own some ammunition, except that some have been specifically restricted because they have been commonly converted to modern ammunition. You can own a smooth-bore muzzle-loader of up to 2" bore on a shotgun license (which is easier to obtain than a firearms certificate - FAC). Whilst you cannot buy ready made slug shells for a regular shotgun without a FAC, there is no such restriction on owning loose ball, powder etc. Some forces have asserted that loading a muzzleloader with loose powder and balls turn it into a firearm requiring a FAC, but the law does not appear to support this assertion, but good luck arguing that at the point of arrest. Recently certain brands of smokeless powder were reclassified as requiring a special license to own, but the orginal formulation does not.
We have laws covering specific prohibited melee weapons and these are almost exclusively a result of some highly publicised incident by idiots. Whilst the intent is clearer, sometimes the implementation is almost random. Under a strict interpretation of the law I can own a sharp full-sized rapier, but not certain types of cheese knife. Most of these are mitigated by the "reasonable" defence. I cannot carry any knife larger than a non-locking penknife "just because". I can carry even a large knife or sword if I have a good reason. The reasonableness will be tested in court so again it won't necessarily stop you being arrested (though if you can convince the police officer that you have good reason it may not get that far). A muster out weapon might come with a built in good reason "this was a personal gift from the sector baron - I am required to wear it as part of my uniform"
It should also be remembered that not all officers of the law actually know the law or they may be operating on "local" interpretations or might be bringing other baggage to their judgements. A pragmatic officer that is about to go off shift might be keen to avoid the paperwork, but an overly zealous officer, in the midst of a messy divorce and who also really doesn't like off-worlders, especially the mouthy type he is currently dealing with, might be looking for a scalp.
Real legal complications are not neat distinctions and LL is pretty clear cut because it is a game. Personally I like the randomness to keep players on their toes. Visitors to a new world should always be wary about tripping over some local regulation that they either did not understand or even know about. It is the referee to make that interesting rather than irritating. When you get hassled outside the starport, the actual LL might be less important than the characters attitude, which ensures the player has agency and the disposition of the authority you are dealing with, which ensures the referee retains fine control. If for plot reasons you want to take that high tech laser weapon out of the game temporarily then a slavish adherence to Law Level should not prevent you. As long as the player isn't permanently denied their cherished "Best Gun", you are not required to allow players to dictate the terms of the adventure.
The story is in that specific interaction with the law enforcement officer, not in the technical difference between a self-loading pistol and a repeating pistol. That will come out in the court case and that probably isn't the adventure you or they want to be having.