Full Screen while playing animation in Scene

I am using Animator Timeline Editor to animate a camera moving across a field. When the animation plays back, I record it with FRAPS (since there doesn't seem to be a way to render the animation to a video file). The only problem is that when Unity is "full screen" it's not really full screen. I get the menu bar at top and gray bar at bottom.

Is there any way to make the animation play at true fullscreen without the menu so I can record it for use in a projected animation on stage later on?