I assume you are not allowed to copy music files to your hd at work, which is why you play them from a portable hd?
An iPod is essentially a portable hard drive. iTunes is a stand alone product that the iPod integrates with to make it easier to manage.
You build playlists from your library of songs. When you transfer the playlist to your iPod it transfers the songs for you.
If you install iTunes on your computer at work it's the same concept as running media player with a portable hd. Plug in iPod and iTunes launches.
If you can't install iTunes at work then the iPod should still show up as an external disc allowing you to use media player with it same as you were doing before.
Here's a good quick tutorial.
http://forums.livingwithstyle.com/t90029-ipods-without-itunes.html
or
http://www.apple.com/support/ipod/tutorial/ip_gettingstarted_t11.html
http://www.redchairsoftware.com/anapod/
Also WinAmp 5 has a plug-in called ml_iPod, which allows you to manage your iPod from the WinAmp Media Library
Scott