Disclaimer: I am not a UX expert
Cursors, Et. Al.
My thesis is that you should indicate a clickable area in other ways -- don't use dummy buttons.
My approach is to change the cursor to indicate something clickable. That, obviously, doesn't work for touch-based devices. Other answers here have provided some excellent ideas for visual design-based approaches that are more appropriate if you service touch-based environments.
Certainly cursor change can only help improve things, so I would definitely use it (in addition to other visual design cues).
We've actually tested a similar concept on our site and what we found was that when we put a dummy button, new users would only click in the dummy target area and old users would complain that the new button was "too small" indicating that they were discarding their prior knowledge about the entire clickable area.
My conclusion is that if you put a dummy button, it will largely defeat the purpose of having the entire box clickable.
Perhaps some greater UX contributors will provide more alternatives, but I think you should reconsider a dummy-based approach.