I've done some electrical model plane flying. Less power and endurance than combustion but also less noisy and smelly, which means you can fly around in more places.
Anyway, electrical engines for model planes are a bit different from the fan in your pic. First of all, they are cylindrical and small so that they can fit in the fuse with a small cross section. See here for a pic of a typical engine:
http://www.kyosho.com/accys/kyog1922.html
Their RPM is also typically higher than fans. As far as I know, most desk fans are well under 5000 rpm, while here we are in the 16000-28000 rpm range. Granted, you sometimes use reduction gears (hey, just like in a real plane

) but still.
Finally, the props are more like airplane props. See here for pics
http://www.kyosho.com/accys/kyoq0104.html. Thin blades with tapered edges for the reason stated by Slamclick and QantasA332. You want to push the plane, not the air.
Electric model planes tend to be underpowered (or battery life would go under the already low 10-20 minutes you get now), and the best application is motor assisted gliders such as the lovely Stratus
http://www.kyosho.com/airplanes/kyoa1080.html. Note the foldable prop so you can land. Basically there is a tradeoff between power and battery life which hand held fans need not bother with.
So my advice is, buy real model airplane parts. They are built for this. Your fan seems much too small and heavy. As for the pusher prop idea, I don't see why not.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo