Hello,
It is possible to hook up some wires to the TinyZero for a distant switch. To do so, however, you need some pretty careful/small soldering.
I attached an image of the power switch on the TinyZero with some pins colored. The two switches that you would need to solder to are red and yellow in the image, the other 5 pins of the power switch are all connected to ground and are boxed in black to show this. I also tossed in a reference to the schematic with the colors coordinated to offer some background explanation.
So, yes it is entirely possible, but you need to be careful when soldering pin 2 (yellow) because it is very close to a ground pin on the left. If you were to short, or solder, pin 2 to the nearby ground pin - things would blow up when powered and effectively ruin the board.
So tread carefully as you solder!
Thanks,
Réna