If you talk to hesitant people, and there are a lot of them, the reason is a mistrust of the people leading the effort and managing the pandemic. Why mistrust? Many reasons, but the most challenging one is because of numbers that don't pass a smell test coupled with apopleptic ad-hominim aggression directed against anyone who questions them. This all but guarantees a 20%+ rejection rate from people who just dig in because they do not make health or other decisions based on fear and shame. There will be a defiant group of about 5-10% who you just can't reach at all, so if your plan needs them, you will need a new plan.
Calling people hesitant is patronizing and was probably the stupidest PR move of all time and the committee responsible for it will have to live with those consequences.
But instead of arming people with a litany of whataboutisms, I would say this to an unvaxed person: given your objections, how does getting the shot prevent you from resisting or even fighting a battle you percieve you need to fight against these authorities you do not trust? Polite euphemisms aside, let's call it what it is, because that's the crux of it.
If it does, you need to just act now and literally overthrow your governments in the next few weeks, but if you aren't going to act today and do that, then get a shot, and use the time to figure out how to depose these people that you do not trust in good time. If, as many hesitant people believe, there might be long term harm to them, your long term still involves a conflict to replace these people, but risk from hypothetical side effects still nets out of that equation.
My rationale to the so-called hesitant would be this: get the shot, and then use the time to organize and support your revolts against untrustworthy leaders and institutions, because once you are vaccinated, you can draw from the ranks of others who were also forced into it. Use this to unite people to your causes against untrustworthy authorities, because your skepticism comes directly from people using this to divide you. Take that from them, and then commit to organizing and scaling the change that has to come. Having the shot gives you skin in the game with the people you are going to need on your side.
This issue isn't the main battle, but I will absolutely support efforts to ensure trustworthy people get into positions of authority after this.