Often a controversial subject, weapons -- manufactured or improvised; officially permitted or otherwise -- are a fact of life that will need to be addressed.
The lunar settlements will have a different set of values and a different culture. Even though that on Earth the view on weaponry is diverse and controversial, the lunar civilization might choose to ban the right to bear arms.
Based on the fact of the evolution of the economics system the lunar colony will have a different set of economics that might resemble the capitalism on Earth. However, since the resources at the beginning of the lunar settlement will be scarce, the private property might disappear and then, the use for weapons to defend the mentioned property. Also, the definition of crime and illegal would be subject to the future lunar culture. And with that, the necessity to enforce law through the use of force.
As the population increases and gets less heavily controlled and pre-selected, the more the problematic aspects of nature might become unavoidable. When this happens, weapons might become necessary to give people power to prevent a tyrannic government, defend private property, enforce law, etc.
Initially the question of what small arms to provide for is unlikely to matter as situations outside of Earth's atmosphere where weaponry is going to be needed are at least initially going to be highly improbable.
The real problem arises in the question of what weapons are suitable. It would be less than optimal to carry large calibre slugthrowers for use in a pressurized hull with hard vacuum on the other side and potentially dozens or more people at risk of decompression from even an accidental discharge. Furthermore, bullets bounce all over the place. even shots fired from air pistols exhibit unpredictability indoors.
Edged weapons may be okay for most environments, but those often support the physically strong. Grandma can't protect herself with a sword as well as she can with a terrestrial .357 magnum.
Specifications for Ideal Solutions
All guns and explosives are extremely dangerous in a space settlement, then, all lunar weapons might have these specifications:
- Safe for use inside pressurized compartments
- Minimal or at least reduced ricochet risks
Tazers, Mace and Pepper Spray are legal to possess in the USA, but illegal in Canada and most of Europe. However, the legality of those might be a totally different issue on the moon.
See also Right to Bear Arms