The Technical Answer:
Zimbra has a desktop application that, I believe, uses SOAP to connect to the server and retrieve message and other data without POP3 or IMAP. Darn it all, I can't seem to track down hard documentation on that though. Nonetheless, check out Zimbra Desktop.
The Softskills Answer:
This is not in direct answer to your technical question, but is added for you and anyone else reading this in the future to consider the larger picture.
It sounds like you are either not part of IT or you are not in direct contact with the system administrators. It certainly appears that what you're doing is either against IT policy or at the very least not being done with their approval. If that's not the way the situation is, then perhaps it's a language / thought barrier between us.
Consider a few simple ideas:
IT personnel should be asked for help first. Not because you are incapable of finding a solution on your own, but because they are the stewards of the systems and will likely know the ins and outs of properly setting up services and applications. Building bridges with IT people is usually a good thing, no matter how surly and unreasonable they are. If they see what you need, they can (or at least should) properly address the situation.
IT rules are not challenges. As such, you shouldn't seek to subvert them. Not because IT is in its ivory tower and shall not ever be questioned. Rather, because this is a personnel issue that should be handled by managers. Solving personnel issues with technology is like bailing water on the sea floor. Seeking to find a technical way around the rules will start an arms race between people and departments. Talk to your manager to get things changed.