I've technical reviewed 3 books and still don't have a way of saying that that doesn't sound awkward. For those 3 books, the production manager sent me Word doc files by email, which I would comment on, rename with my initials at the end, and then send back by email. I've also sent copy edits as pull requests on GitHub, with comments in the commit message, and sometimes a back and forth with the author in the pull request or issue queue.
I'd like to see more books posted to GitHub, so that people can fork and submit corrections to and submit issues. I've contributed to The Little Redis Book (just copy edits here and there) and loved the process. I've seen this with technical books, and would like to see this with less technical topics.
Advantages of this approach:
Some barriers to this happening: