Around 20% of people have a fear of needles. Around 4% have a clinical phobia, often intense enough to induce fainting.

I suspect a lot of "vaccine skepticism" is just an expression of such needle phobia.

Maybe developing more needle free vaccine delivery mechanisms would solve a lot of this problem. I have much doubt about arguing people out of phobias.

I don't see any evidence that the level of fear of needles is different now from what it was 10, 20, 30 or more years ago, so it is hard to see how it could be a significant factor in falling vaccination rates now.

It's not. It's scientific ignorance combined with lies (Wakefield) and misinformation. There may be some small percentage of people who completely avoid injections but most people who understand vaccines accept the benefits outweigh the short term fear / pain of needles.