Yes, I know what you mean. Sharing a Google Doc or Drawing, and seeing visitors actually using your stuff is not so weird for the creator, but it sure can be strange when you're viewing someone else's stuff and you notice other initials, actual faces, and anonymous random animals popping in and out while you're there! It's kind of like accidentally walking into the a bathroom, and seeing someone of the other gender in there. For a moment, you freeze, thinking that you've looked in on something you're not supposed to be seeing, and then you realize it's not you who's the one out of place! Ok . . . the comparison may not be quite that drastic, but it's close.
To solve this problem, here is what I would do: download your document (or drawing, or presentation, etc) as a PDF. In whichever Google app you're working, if you click on the File menu, you will see "Download as . . . " Choose PDF, save it wherever, then just attach it to the email you send. Alternately, drag that PDF back to your Drive, then share the link to that file (instead of sharing the link to your Drawing itself). Any links you may have included in the newsletter will still be live, AND then each viewer will be looking at his own copy of it; ergo the faces won't pop up.
Click here to see a great example of just such a newsletter, created by Billings' Extended Studies teacher, Jennifer Williams.