There are actually 2 setting areas:
1) is the configuration folder %apdata%\Roaming\calibre. This is YOUR preferences on view, devices and plugins...
2)Is part of th metadata.db, which is how
that Library is configured
To make a blank Library that mimics the existing one:
right click the Library Icon: Create Library: Create EMPTY LIBRARY:
Tick Copy Structure from the current Library.
This copies EVERYTHING you set about that Library into the db. Just copy the WHOLE folder that has the db to the new machine. then you can switch to it.
How locked down? Could you run Calibre Portable from a USB drive/stick? (Caution: do not violate company security policies that could result in termination or jail.)