Wiring things in takes care of that
I have my detector mounted on velcro at the lower left side of my windshield which, in NJ, allows it to "hide" behind the inspection sticker so it is not obvious from the outside. I have the adapter plug wired into the fuse box which is directly below in the foot well, and by using a circuit that powers on with the car it assures that the detector is automatically powered.
The wires are very easy to run up the side and they come out just at the edge of the detector, so they are hidden behind the dash and out of sight and out of the way. You could certainly wire any detector this way, even one that you mounted by the mirror. As for that, I wired my remote mic for my installed cell-phone by the mirror, so all you need is enough wire. Just depends upon what is most effective for you and provides the level of "stealth" you want. Don't do the battery thing, you'll regret is someday, in a big way.