I've had trouble booting recent versions of OS X from my iPod, and perhaps Panther will be unable to do it.
In any case, since the Installer doesn't work when it's not on a CD or DVD 9 (there may be a workaround, I don't know it), and you cannot run the Installer without booting up from it, the only way to do this is:
1) Take a computer in the lab. Prep a partition or format it, and install the OS you want on this partition. I assume you don't want to merely upgrade the campus Macs, but install it clean.
2) Start up the comp on Panther, go through the motions, and install whatever school-specific software you need. Clean up the install - make it as close to what you want on the campus Macs as possible. Repair permissions, run Disk First Aid, etc.
3) Install Carbon Copy Cloner on the new Panther partition.
4) Run the "Restore" command of the iPod Updater on your iPod. Go through the iTunes loop, checking "Allow hard disk use"
5) Clone the new Panther partition to the iPod.
6) Test it - shut down your Mac, unplug the iPod, replug the iPod, start up the Mac with the Option key depressed, and <the moment of truth> choose the iPod as the startup disk.
7) If the iPod boots, you're golden. Now all you need to do is go a new Mac, prepare a partition or format it, plug in the iPod, clone the iPod's data to the new Mac, and start up the new Mac.
This idea has worked for me for doing complete archives of my system when I was mucking around with learning Unix and regularly breaking it

. It's useful for making a most-recent-version startup disk for Norton Utilities (older versions, like those on an install CD, tend to throw everything out of kilter). It may or may not be good for you (I mean, you may have license issues with dozens of comps running the same stuff.