You should give [pdfPresenter](https://www.pdfpresenter.de) a try. It's an app for the mac that allows to present pdfs like in powerpoint. However, you can use handwriting to annotate your slides. You can make use of two logically separated writing surfaces, one visible to the audience, one only visible to you.
I use it for teaching math the following way:
- I have my theorems and the like on a slide (prepared using Latex and beamer class), however, no proofs or examples.
- For the proofs and the like I use the invisible writing surface to make a preparation for myself. The surface is not bound to the size of a page but can be scrolled down arbitrarily far. Thus you have as plenty space as you need, like on an infinite blackboard.
- In class I show the theorem and develop the proof along the invisible handwritten notes I have prepared.

I have checked: You can share the screen used for the projector by zoom. This way you can stream your presentation and keep your notes and annotations hidden. However, this only works if an external monitor is attached to the mac, at least I was unable to get the presentation shown any other way. 

For handwriting you should use an iPad, writing with the mouse is pain in the neck. The only obvious downside of the app is that pdf-slides can't be changed within the app, but for me that's fine.  

Everything written can be saved/exported to pdf. This way I can hand out the outcome of class to the students.