Karl,
If you are running WinXP, then I think you can configure stuff under control panel/windows firewall and perhaps turn off the nag. Also, turn off or reschedule windows update in control panel.
I'm still running Camsoft on Win98, and on that PC, I did not even install IE when I installed windows. That will keep the darn thing off the internet However, I do have it running ok on the local LAN and can transfer files from another PC which does have internet access. I'm not sure if something like that would work for you.
You're right, I would never want any AV crap running in the background when the machine is running. Most antivirus programs can be configured to never scan your drive, and that is the setting I would use. That way, I would say when to do the scan.
Also, turn off the AV auto update feature, if it is there. Come to think of it, I don't know what AV you could run without internet access, but perhaps you could virus scan a remote computer through your LAN. That I have never tried.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)