Kind of depends what you are putting in your CP. A Tron style joystick and some spinners have a lot of hardware "below deck". Most buttons and joysticks only require a couple inches.
Happ's web page has dimensional drawings of most of their stuff, so that would give you an idea of how much space you'd need. Also, some stuff (particularly track balls and joysticks) can be recessed into the wood a bit (I'm assuming 3/4 plywood or fiberboard here), buying you an extra 3/8 - 1/2 of an inch.
Also, not all keyboards are created equal, so look for one with a lower profile.