Unless I have misunderstood the question, my own app JetReader does this. It lets you select a folder on your phone that acts as your library, and reads books directly from that folder (since you have given the app permission to use that folder, it can do that). It does create some temporary files and some cover image thumbnails inside the app folder, but the books are not copied there.
However, when doing this on my own phone, it looks like I can only pick a folder in certain parts of the file system. So I cannot guarantee anything. Have a look at the web page, and let me know if you want a promo code that you can use to redeem the app for free if you want to try it out.
https://jetreader.net