Your camera has not been damaged at all.
The battery is not heavy and 20cm is not a great height. Moreover it seems that you are unable to find any fault with the camera.
I have dropped my camera 3-4 times. It has some scratches but it is in perfect working order.
If you know it hit the button, as long as the button is still functioning, there is not much to worry about.
Apart from that, take some photos and see if anything is wrong with it, check the focus and try to listen if the camera is making any unusual noise.
Finally, it is worth knowing just how durable a DSLR can be. People have put it in some extreme conditions before, in hot dessert, in sub-zero environment where ice forms on the camera and the cameras did the job just fine.
Here is a video that shows how durable cheaper DSLR can be, it may be a PR stunt but it does make it clear that DSLR need not to be treated like a baby.
Apart from that, pro photographers had reported some amazing stories about how their camera fell / get ran-over by a car / bitten by a lion / attacked by a black bear and surprisingly the cameras were either still working fine or only needed rather minor repairs.
Personally I have dropped my camera from chest-height, waist-height, with and without hood, on to wooden floor, carpeted floor and even rock-hard dry pavement.
I got nothing more than scratches.
It also had been in slight rain, sometimes mud covers it, sometimes it is powdery dust etc.
Everything just continued to work.
Protect your camera as a tool, not as a fragile egg. That way you worry less about damaging it and focus more on creating photo, and your camera will serve you just fine.