I'm using a moto X Pure and a small Bluetooth controller. I find it works in games that have controller support but nothing made just for cardboards, like the cardboard demo app itself. The controller I'm using is similar to this one:

https://www.amazon.com/dp/B00UJC2KW0/ref=cm_sw_r_other_awd_Tm4fwbPFACA2M

Those actually have a mouse function http://www.amazon.com/BEBONCOOL-Wireless-Bluetooth-Controller-Gamepad/dp/B00UJC2KW0/ref=sr_1_4?ie=UTF8&qid=1444823668&sr=8-4&keywords=bluetooth+gamepad . Not sure if limited only to Android, though. You have to press some buttons to get there, so I always refer to the (not very user-friendly) manual. Having a mouse function means you have left mouse click in Cardboard apps.