You can crop them, but there are limitations, so you will see most HTML5 video players , just use the built-in controller.
For example, you cannot run full-screen mode on an iPad through javascript. Thus, you cannot create a custom button in HTML that calls it. You can only do this through the built-in controller (or reverse pinch). This is the unfortunate limitation of mobile Safari.
In addition, once in its own full-screen mode (browser or mobile device), the controls by default accept anyway. Therefore, in the case of the iPhone, which always plays in full screen mode, in fact there is no use for creating custom controls.
Mozilla (Firefox) actually takes an approach where developers can make any element on the page expand to full screen. This means that user controls can be saved even in full screen mode. I really appreciate this direction. I have not tested whether this still works in FF4, but this is apparently a plan.