"Wired Wireless" Intercom System

Yes I know... anyway here is the question posed to me.

The largest problem with the current wireless system is that the batteries just do not last, particularly during cold weather. He (referring to a committee member) suggested that it might be possible to install a "wired wireless" system, such that the device outside could be connected to a wireless transceiver mounted just inside the door. There is, in fact, AC power within just a few feet of the current box (and maybe 2-3 feet farther from your proposed ADA location) via the supply to one of our emergency exit lights (added after construction). If AC power could be drawn from that supply, we might be able to eliminate all the uncertainty and much of the effort involved in trying to fish wires from the door to the main office. Alternatively, one could probably fish a power cable from that tap directly to the outside device. Our property committee chairman seemed pretty sure that this would not be difficult.

Comments? Unforeseen objections or problems? Cost implications for equipment?

Does anyone know of any device like this?

Background: A local church is currently using a "wireless" intercom system. They say that the cold weather seriously effects the batteries and they have to keep instalilng new batteries. They have requested a quote on a wired system. The problem is, the way the church is built makes it more time intensive to get cabling from the transfomer to the office as well as the front door where the intercom will be located. Currently they have the wireless mounted on the glass. My suggestion was an audio intercom and included a video intercom to consider over the audio intercom. Mind you, I have offered the components at my costs so it's a really good deal.

Any ideas/suggestions/anything would be greatly appreciated.

The white thing on the glass is the current intercom.