As theducks says, I assume this will be a library of Public Domain or Creative Commons-licensed books.
You can download Calibre Portable from calibre's website, and I assume WINE won't have a problem running the self-extracting installer executable.

Just copy the library you created so it is in place of the "Calibre Library" folder in the portable install.
The only problem you may run into is pathname issues, since linux is case-sensitive but Windows isn't.
The problem is usually moving from Windows to linux though

anyway, I'm not sure WINE will share Windows' "different"ness.
If you don't want to use WINE, you can probably use p7zip to extract the exe file, unfortunately, I have no idea what will work properly since calibre uses a custom exe, not anything NSIS/InstallShield/Inno -based.
And I didn't move all the way to linux just so I could go around extracting Windows programs on my linux box!

So I've never actually attempted to try it. The above "wisdom" comes from the Arch Wiki section on
trying to package non-free usually-Windows programs, which helpfully describes some common ways to extract Windows EXEs.