Without knowing the exact software you'll be using it's hard to say for sure, but as andrewc has pointed out a lot of software will snuggle up very closely to Windows and bury itself all over the place, so it's doubtful you'd get it run from from an external drive without it being installed in the laptop's OS. And if your IT department are worth their salt, they'll know what you've been up to as they'll have automated reports running on installed software, patches, etc.
I know we used to when I was doing that sort of thing. Always funny to hear people plead their innocence when I've got a screen in front of me telling me exactly what's on their PC, where it was installed to, when it was done, etc.
I'd say it's probably better not to risk it, especially if you've signed any sort of agreement where you agree not to install software on your work's laptop without prior approval from IT.