I think the current cardboard best practise seems to be to avoid using the button and use gaze based controls instead. My game this time last year was really simple and didn't really use any controls other than tilting the head slightly forward to walk so it's possible to use no controls at all.
This time around I'm using a Bluetooth controller because I want arcade style controls seperate from the headset.
As for headsets if you've used the base handheld carboard for more than 10 mins you'll know most people interested in using it have spend the tiny amount a headset with a strap costs.