The area with the hose in it currently is your return area. The water level will fluctuate in this area so that's not good for a skimmer. Like you said, the refugium area is the largest area, and you have that skinny area opposite for I don't know what. I'm assuming the smallest area is where you would have the tank draining into it, then it flows over both the skinny area and the refugium area to the return area.....sound right?
/IME, a protein skimmer is much more important than a refugium, so I would make finding room for that my first priority. Could you use the long, skinny area for the refugium and use the largest area for the skimmer? Measure both of those.