Yeah, so if this is a standard 12v wire you're running, try prying off the door trims. I'd bet good money there's at least a half inch of space somewhere in there you could run this wire through to the outside, possibly leaving a small connector inside the wall that you just plug the solar panel and battery into when in use. Something like https://www.harborfreight.com/solar-power-connection-cable-kit-59171.html one of these kinds of connectors. Then just carve out a tiny bit of drywall to allow the trim to sit flush, recaulk and you're in business.