For live demos, I use Airplay to mirror the display to an AppleTV. For online demos, I use an app like AirServer or Reflector that make my laptop an Airplay-receiver and then share my desktop/screen over G+ hangout.
I highly recommend adding the "Fingertips" Cocoapod to your project and it will highlight finger presses and taps when it detects you are using an external display. You just need to replace your UIWindow with MBFingerTipWindow.