Looked at it - Pipe diameter is closer to 6", and has a 4-5" pipe inside it. The furnace/ac, of course, is directly below. That would all come out, the duct work would come out, and the pipe would go straight up. I'd actually like to take out the walls of the "closet-type" area that it shares with the water heater. That area is in roughly the center of my 765 square foot semi-shotgun house.
The optimal "through the wall" location is in the living room, which is at one end. Bedroom is the other, of course.
Construction is concrete block. I would eventually like to cut a door in the bedroom to the back yard area, and put an add-on deckroom there. The existing "back door" is to the side, but is unused. No knob, no nothing on the outside. Not a hazard, because all I need to do is lift the crossbar.