So I designed a first model, 3d-printed it, and hacked it around a motor of a conventional fan.

And it works!

First, I was very surprised that the rotor itself works like a fan, with no stator. The blowing is quite directional, closer to being axial than radial.

Then, when I've put it all together, I did a rough comparison with a similarly sized fan (the one on the photo)

Free-standing:
* the amount of airflow feels comparable, the conventional fan is probably doing a bit better
* the amount of noise is similar, but different whine frequencies (my one makes a higher-pitched whine
Blocked:
* the suction of my fan is substantially better
* my fan makes much more noise when blocked. And compared to conventional fan, which starts to spin faster when blocked, my one slows down instead.
All in all, I think this crude attempt worked absolutely fantastic! It was just a quick test to see if it wound make airflow at all!