I have tested this, because I needed a short and very flexible HDMI connection.
The length of my ribbon cable is under 10cm using only 13 wires.
The resolution i have tested is 1080p.
If you're fine with some pixels or sometimes horizontal lines caused from interferences, this solution totally works.
At worst sometimes my monitor turned off for a second.
If you want to have better video quality wrap the ribbon cable in aluminium foil and secure (cover) it with electrical tape.
I dont know how important it is, but I also soldered the aluminium foil to the shielding on both ends of the connectors.
This way at 1080p, I get a sharp signal to the monitor without noticing the slightest interference.
As for soldering, 13 wires at pins 1,3,4,6,7,9,10,12,15,16,17,18,19 are enough for the connection to work properly.
I initially used a smaller ribbon cable before (about half the thickness), that did'nt work out well.
A ribbon cable about the thickness Blamoo showed in the question is enough for me.
If you need HDMI to mini HDMI you need to swap some pins, even if the pinout is (almost) the same.
Be warned: if you do this wrong you might fry the connectors (happens to me)