VNC for the Mac could let you project and control the mini from your laptop over the network. While great for some things I feel that for CAD and more it's not a viable solution. You can't connect the video output from the mini to your laptop because there is no compatible input on the laptop.
Since "it's work" related why isn't this a work expense? Let them pick up the tab?
I run ArcGIS (at work on windows) which only could work on an intel mac. I have a year and half-old powerbook G4. I don't want to buy a whole new system to run one app. though I have considered buying a mini. Could I theoretically use my laptop as the display and keyboard for the macmini unit?