Hey Jules, you can set up an external screen (this case your projector) in two different ways: Mirrored, or as its own screen space. You can change this under Displays in System Preferences, or you can switch between the two quickly by pressing CMD+F1. If you set up the projector as its own screen, you can drag an app to that screen and show that to the audience while you do something completely different on your own screen.
You can of course yank the cable out while you get organized and then plug it back in. Depending on your projector's settings, it should work just fine.
Keynote is great but I haven't used it much so somebody else might be of more use in that regard.