In Ancapistan, only things that violate the non-aggression principle are illegal. Normally assassination violates the NAP, but there are important exceptions. For example, suppose someone commits a crime so heinous that the private court system decides that his death would be appropriate recompense for the victim. However, before he is executed he escapes and moves to some state-controlled territory where nobody has any interest in bringing him to justice.
In this case, it is ethical to hire someone to go find him and kill him. So, Ancapistan would likely have assassination companies. In the long run it would not be a big market, but in the short run it might be big business.
The reason is that the first free societies will be threatened by nearby governments. A society based on anarcho-capitalism would prefer not to pay for a standing army to protect itself from these large, criminal organizations. Fortunately, there is a much cheaper solution. Instead of fighting an army, you can just threaten the political leaders who control it. If they send an army to attack us, we will send an assassin to kill the political leaders.
How much would an assassin charge for killing a politician who sent an army to attack the place where he lived? I imagine many people would offer deep discounts after seeing their home bombed or their family members killed. I also imagine many libertarians would be happy to pay a small yearly retainer to an assassination fund so that assassins are ready and well equipped. The United States spends over 500 billion dollars on its military. A highly effective assassination company would need many orders of magnitude less funding.
This also reveals one of the few benefits of democracy. Politicians in a democracy need to be well known to garner votes. This makes it clear who should suffer retribution for attacking a libertarian society. In contrast, libertarian assassins can remain anonymous and take payment in cryptocurrency. Jim Bell details this idea in his essay, “Assassination Politics“.
Furthermore, this should be a relief to those anarcho-capitalists who hate nuclear weapons. Some libertarians argue that in order to deter nuclear attacks, one must threaten a nuclear counterattack. However, there is no need to kill innocent people to convince a government to keep their hands off the launch button. Similarly, there is no need for weapons that can defeat large armies or navies. A libertarian society can protect itself simply by sustaining a credible threat to the leaders of any government that intends to do them harm.