But it appears there is a solution if you can access a thumbdrive as in my case. Most thumbdrives has U3 which allows you to run software of your thumbdrive, but there is maybe an even easier solution. Most open source applications that have a Win32-port can be packaged to run of a thumbdrive. The most famous packaging sites for this is PortableApps.com.
Officially I don’t install any software on a machine and I don’t break any company policies. I doubt how long it would take before CD-drives and USB-connectors are closed again due to dataloss or stolen data. But then again, they could also offer a proper browser. It is also good to know there are companies with even stranger policies and solutions. Security should be about enabling people not trying to stop them as they will work around the issue sooner or later to get things done.