In my essay Let's Divide Law-Enforcement: Natural Law vs. Positive Law, I made the case that law-enforcement should be divided into two separate parts—a security force linked to insurance for the protection of persons and possessions against aggression and theft and a police force for the enforcement of rules and regulations enacted by the community. This would mean that the people who enforce traffic laws, drug laws, and gun laws would be entirely separate and detached from the people who respond to burglaries, domestic violence, and such. I also suggested that laws should be made directly democratically and that both divisions of law-enforcement should be subject to, and accountable to, public courts, tribunals, or judges. I personally prefer a system of trial by jury, following the recommendation of Lysander Spooner. (Cf. Lysander Spooner, An Essay on the Trial by Jury)
Reforming law-enforcement along these lines would set us up to eventually be able to disarm police like they have in England, New Zealand, Norway, and elsewhere. The security guards who protect persons and possessions need to be armed, since they respond to violent crime. However, police officers that enforce arbitrary rules and regulations, rather than responding to violent crimes, would not need to be armed most of the time. If the police need firearms to raid some building in order to enforce certain community rules, they could be given firearms to do that, but the police that patrol the interstate would not need to carry. I don't think that it would be wise to immediately disarm police. You would have to wait until public anti-cop sentiments change. Within a decade or so, public sentiments would change as a result of these reforms in law-enforcement and people would generally like police officers, so the police would be relatively safe doing traffic stops and crowd control without carrying firearms.
In order to disarm police, I think we would also need to implement sensible rules for gun-ownership. Everyone should be allowed to own a gun, theoretically. However, there should be certain requirements that one must meet. In order to get a license to operate a motor vehicle, you have to pass two tests, a written test to prove that you know the relevant laws related to operating a motor vehicle and a driving test to prove that you are capable of safely operating a motor vehicle. There should be similar requirements for gun licenses. Just as there are drivers education courses, there should be gun education courses that teach you when it is legal to use a firearm and when it is not. These courses should also teach you how to safely handle and fire a firearm, as well as emphasizing safe storage and maintenance practices. It might be desirable for such classes to be mandatory in order to get a gun license. Even if the formal classes aren't mandatory, it should be mandatory to take both a written and a shooting range test in order to get a license. If you don't know when it is legal to shoot, you shouldn't be allowed to have a gun. If you can't control your firearm and hit your target, you should not be allowed to fire it. It might also be a good idea to register guns like they do with automobiles.
When thinking about gun regulation, suicide is a big issue that we should focus on. It is the second most common cause of death for people between the ages of 15 and 34 in America. It is within the top ten causes of death for people of all ages. And 60% of gun-related deaths are suicides. More than half of all suicides are carried out with a firearm. Most suicides are entirely preventable and suicide rates drop when firearms are harder to acquire. And most people who attempt suicide and fail do not attempt it again, indicating that most gun suicide victims were likely going through crises that could be worked out with counseling or other tactics. These are victims that could have easily went on to live happy lives. Requiring counseling and mental health evaluations for people seeking a gun license would help prevent suicides. It might also help prevent mass shootings and gun violence. It would also be desirable to prohibit people with a history of violent crime from getting a gun license, especially if their crimes involved gun violence.
Having sensible gun regulations is a prerequisite for disarming police. And disarming the police is a prerequisite for having a safe and libertarian social order. That being said, everyone that wants a gun license should be able to have one, provided that they know the law, obey it, and can safely operate a firearm. In order to buy firearms and ammunition, you would have to show your license, like when purchasing liquor.