You can be a fully practicing physician in most fields without much procedure involvement, except for surgical fields, of course. But once you finish residency in internal medicine or most of its subspecialties, family med, radiology, pathology, psych, pediatrics, you may not have to do any procedures if you are in the right setting. You can also do these fields and do lots of them. The trick would be getting through residency without doing them, and that to a large extent depends on where you do your residency. Some IM programs have limited exposure because nurses do a lot, PAs do a lot, other specialties do them. But other programs have you constantly doing things.
I'm in path, I have very limited procedural exposure during residency, and didn't have to do a prelim year either. I had to do a few FNAs. Autopsies, yes, but those are on dead people so you can't really screw much up. Some path residencies have you doing lots of BM biopsies but not mine. Frozen sections can be tricky, grossing in specimens, but it's hard to hurt someone directly. My experience when people are asking about fields where they don't have to do procedures is that they fall under one of a few categories
1) They have limited dexterity (shakiness, whatever)
2) They just dislike them
3) They're scared of hurting someone.
And frankly, many people in the second category (at least at first) are just projecting or are in denial and actually belong to category 1 or 3. To be honest, you have to get over your fears. Very few people shake so much that they can't do simple procedures. And you are unlikely to severely hurt people if you are careful and learn correctly with supervision (instead of being avoidant of them).
I hate procedures. Mostly because I find them tedious and uninteresting. I don't really get a kick out of doing them like so many others. I have a bit of a nervous tremor and initially I was worried about how I would deal with procedures, but I dealt with it just fine in med school. I wouldn't trust myself to operate on small vessels but I was fine in surgeries when I had to sew wounds and cut things and all that. But very few people are skilled enough to do microsurgery, whether you shake or not. And sticking needles into people wasn't as difficult as I thought.
So ask yourself why the procedure aversion. If it's simple fear, discard the fear (or simply just confront it) and just do some procedures and you'll find you didn't need to be worried. If it's dexterity, do them anyway with supervision and you'll see you have less reason to be worried. But do not avoid them just because you're worried. You'll only hurt yourself and potentially your patients in the future. A lot of medicine is about confronting your own weaknesses, fears, and anxieties. You become a better doctor by learning what your true weaknesses are (and not simply your fears) as well as your strengths (many of which will be unexpected). You do not become a better doctor by avoidant behavior.