Is it possible to use my window A/C unit without actually installing it in the wall?
You may be able to rig up something whether the compressor-side air intake and exhaust are piped outside, but the efficiency will be low and you may risk burning out the compressor by working it too hard.

If you want something you can install in a small opening, you might consider wheeled portable AC units which come with a flexible duct.

If you're still determined to try it, note that window AC units have two sets of air intake &amp; exhaust:


the "inside" side that takes air from inside (usually through a large filter on the front), cools it, and blows it back inside
the "outside" side that takes air from outside, heats it (with the heat removed from the cool side) and blows it out the back.


On a typical window AC unit the "outside" air comes in through vents on the side and top of the unit and is blown out the coils at the back. So you will need to make sure both of those parts are getting the airflow they need. And they can't be the same duct, or else you will just get super hot air recirculating through the unit.