This will not be the answer you are looking for. Nevertheless, I think it will be helpful.
First, no, there is no way of getting out of presentations without harming your career. You write of presentations:
I do not believe that it should be an expectation for someone in a junior level engineering role.
On the one hand, yes, this is an expectation even of a junior. Others have explained that very well. On the other hand... just why is this expected of a junior? It's expected of a junior because it is expected of a senior, and juniors are expected to grow into a senior role.
Presenting one's work it an absolute necessity. How else can you show people that what you are doing is worthwhile and should continue to be funded? And not all such presentations can be in small, intimate settings.
You may be able to get out of presentations once, or twice, or for three months, or even for two years, using the techniques others have suggested. However, if you and your work are not visible, and if you actively avoid visibility, promotions will not come your way. The very best outcome would be that you would stay in a junior role for your entire career, unless you find an uncommonly accommodating employer. And when layoffs come, and they inevitably will come at some point, you will be one of the main targets for cost reduction... because people will have a hard time even remembering what you do all day long.
Second, here is what I think is helpful. You sound like you have full-blown social phobia, or social anxiety. This is a recognized medical condition. It is most emphatically not a question of "stage fright", it should not be taken lightly, and you have a much better chance of dealing with it with outside help than trying to deal with it on your own.
I think the other answers so far have not identified and addressed this aspect clearly enough.
The good news is that social phobia is extremely amenable to classical cognitive-behavioral therapy. I would strongly recommend that you see a psychotherapist. The therapist can work with you to address your problems with speaking in front of an audience. And it will help. No, you will likely never start enjoying speaking in front of thousands of people... but if you work with the therapist, do the homework and the behavioral exercises, you will be able to do your short presentations without the extreme stress symptoms you have right now.
I know that you asked how to avoid presentations, not how to deal with your anxiety. (Avoidance of the feared stimulus is a common symptom in phobias, understandably enough - but it's not a solution.) However, given the likely large impact avoidance could have on your career, as well as the good track record of cognitive behavioral therapy, I think this is definitely the way to go.
You may (!) want to include your manager in your therapy, telling him that you are extremely uncomfortable in larger presentations but that you are working on it with outside help. (Given the still-prevalent stigma on psychological issues, it may be better not to use the words "phobia" or "disorder".) Ask for any accommodation you may need. Your manager will probably be delighted to see that you are working to overcome your problems and be helpful. I'd recommend discussing whether and how you want to involve your manager with your therapist first.
I have given similar advice at Academia.SE in the context of social phobic grad students here and here. Apparently people thought this way of looking at things was helpful. In addition, I have some very slight professional familiarity with social phobia from some studies I collaborated on.