The underlying problem is obtaining the books. Even if you never register your ereader and never let it go online, you are just shifting the problem to a computer. They loose fine-grained details about what you are reading, but that's about it.

If you understand that and take proper precautions, I would imagine that any ereader that doesn't require registration would be fine. If you never put it online, it cannot accidentally go online. Plus it isn't tied to your name. Personally, I use Kobo. You have to jump through a hoop to bypass registration by modifying an SQLite database. Other than that there are no protections, so you aren't using sketchy software to realize that degree of privacy.