There's a way to install through the local network but it's a bit more involved that I expected. It involves setting up a TFTP server and place files on specific locations. Even then, it may not work with all BIOS/UEFI systems so you'll have to look into this specifically. For more details I suggest reading through these, but note that while ZorinOS is based on Ubuntu there's no guarantee this will work:
https://www.debian.org/releases/stable/amd64/ch04s05.en.html
I'm tempted to try this so I'll let you know if I do and how it turns out. Please do the same if you have any findings to share, this could be very helpful to include in the Unofficial Manual.