For the USB one I don't think it even has the ability to use WiFi in any way, but it seems you might need to install their drivers to then locally be able to set the label size within a system dialog. In my experience, at least for the wireless one, it doesn't necessarily require its own drivers to work, as it works with Windows' built-in printer drivers, and worked well enough for me on Fedora Linux. (But you might have issues with stuff printing in the wrong orientation and have to account for that by rotating your files before printing)

For the wireless one, I think you'll need at least some form of network no matter what, at least for setup. (I do want to clarify though that you can still use the wireless one with a wired cable to send files to print to it, and as far as I can tell that works even if WiFi is off) They really want you to use the app, but since it really is just another way to access the web UI, they do also just have a guide on how to do it without the app.

I set mine up on my WiFi network that does have internet access, but theoretically since the UI is on a local IP it should be able to work on an isolated VLAN or something similar where no actual link to the Internet exists and it's just a LAN, but I have no clue if it tries to connect to a server anywhere on startup before allowing anything else to happen, so your mileage may vary. It's unfortunately not something I've tested for.

It also has an option to check for updates, I presume to fix any bugs or future potential exploits, but I've never seen my printer update once in nearly a year of owning it. (As far as I can tell this setting can't be disabled, all you can change is if it prints a label to tell you when it updates)

Regardless, as mentioned previously, it should be able to function in terms of just the printing itself with just a cable and no access to the internet afterwards, so you could always set it up on WiFi, add all the page sizes you want, then disconnect it from your network and only use it over USB and it should work fine :)

You can change its IPv4 and IPv6 address/netmask/gateway/prefix length, DNS servers, and hostname in settings, install a custom TLS certificate, etc if any of that helps.

Also, you can change the default print settings, which I personally very much recommend. Depending on what you're printing, you might want to increase the print quality or darkness, particularly if you print a lot of labels in succession that might otherwise start printing a little more faded on the lighter settings.

That's all the info I can think of that would probably be relevant, but if you've got any more questions that I somehow missed I'm happy to answer them too lmao