If this decision is in your control (I know sometimes it isn't), then you might want to rethink whether having the parameters in the URL is truly a security concern. By viewing the HTML source (right-click > View Source in Explorer), anyone can see all the parameter names and values (that aren't user-input). Since the browser is sending this information to the server, there is no way around that, via POST or any other mechanism. It takes a tiny bit of extra work, but that is no deterrent to someone with a rudimentary understanding of web technology; anyone who doesn't have this understanding is probably not a security risk anyway.
I've had this argument many times, with mixed results, but I can tell you that having the parameters in the URL is no less secure than any other mechanism of submitting information to a web application. I'd recommend POST whenever you're submitting form data (particularly if passwords are part of it), but for page-to-page navigation, "parameterized URLs" are fine.