"Waste" a CD, or use a USB "Jump" drive, and stick mIRC onto that. mIRC doesn't need to be installed to use it, though it will stick a note of "last time run" into the registry. If it's okay to use mIRC, but not to download/install stuff, then this isn't an issue.
Note that many work networks prevent all IRC access by blocking the ports, so if that's the case where you are, you won't be able to use any IRC from work... whether it's mIRC or a CGI or Java client (aka: an online client).