Without some extensive research, I will say no. Switches or relays require quite a bit of power, so you would be replacing batteries very often if such a device exists.
So why the "no mains power" requirement?
That is very easy. Some have used a smart outlet, and a relay to build a device to trigger the door.
Couple of examples, there are more if you search. Click "show details" below.
Summary
ZigBee or Zwave on/off switch for garage door opener - #8 by chipworkz
Garage Door Set Up - #2 by aaiyar
Current Recommend Garage Door Opener/Closer - #9 by iskren.p.petkov
There are many dedicated relays/door openers. For example, the Zooz Zen16, but that is Zwave. I am not aware of any similar Zigbee devices, but might exist.
And double edit here, probably every solution you find for door openers will require mains power.
