All this licensed blueprints talk is an overcomplicated solution when an existing system could be leveraged in stead.
The simplest solution is to increase the materials cost of small arms and small arms ammunition and use the existing faction standing mechanism to handle smuggling and arms limitations.
You can still be a smuggler if YOU aren't licensed to transport or carry weapons in faction space, and you can still tie faction standing to that permission without all the overcomplicated nonsense of gun serial numbers and licensed blueprints.
Lets say faction standings work on a -10 to +10 system, and all the overt crimes drops standings, and all the doing missions for a faction raises standings. Standard stuff. You just tie weapon permissions in to that. Note that "weapons" in the following text also refers to ammunition.
*Faction standing below -5 (enemy of the state) shoot on site. Your spaceship can be legally attacked by faction members.
*Faction Standing below -2 (criminal) refused access at faction stations, not allowed to dock or use faction station services, can travel through faction space. Players at or beloy this status can no longer do missions to raise their standings, but may raise standings through other means (like attacking the other faction, or coming to some agreement in the case of player factions)
*Faction standing below 0 (disliked) diplomatic access only (you may not legally carry or transport personal weapons)
*Faction standing 0 (neutral) required to carry small personal defense weapons (Only equipped, and only certain types)
*Faction standing 2 (Ally) required to carry and transport military weapons for personal use (any weapon, limited cargo number of 10 weapons total)
*Faction standing 5 (member) required to manufacture and trade arms (unlimited number of weapons in cargo, can openly manufacture weapons)
*Faction standing 10 (maximum) required to purchase and operate arms scanner
Any faction member with an arms scanner can use it to manually scan cargo holds and players for weapons violations. If a violation is found that player has the option of reporting the violation or seizing the weapons. Reporting lowers the violator's faction standing relative to the severity of the violation and generates a time limited "Deliver weapons to the authorities" job. This job tasks the scanner with delivering the exact amount and type of illegal arms found to a station terminal, for which they will receive a reward in credits relative to the value of the arms collected.
It also creates an optional "surrender weapons to <player name>" job for the person that was scanned. This is a time limited job that requires directly trading the exact amount and type of illegal scanned arms to the player that scanned you. Successfully completing this job allows you regain half of the standings lost when the crime was reported. Completing this job also makes the "deliver weapons" job a required task for the scanner.
Should the scanner fail to deliver arms that were surrendered, they will experience standings loss. Your faction knows you collected illegal arms but did not turn them in.
This means you can smuggle arms if nobody bothers to scan your person or cargo, or if the person that scans you decides not to report it, you know, maybe because you bribed them, but only if you're not so low in standings they won't let you dock or fly through their space in the first place. It also means the scanner can be a 'dirty cop' through a number of creative arrangements involving exploiting the surrender arms mechanics.
None of this requires any serial numbers or limited weapon blueprints.