Cheapest might be to get some 0.5mm FPC connectors. Once you can solder a string, you can do that on 4 times along each edge. Just make sure to get the chip lined up well.
I find that the easiest to do hand soldering this small is to drag a small solder paste stream about 10 mm from the tips of the pins. This makes it easy to run the tip of the iron through it and get just a bit of solder and touch it to a pin. Drag soldering didn't work for me with 0.4mm connectors, as there was to much close copper that was unable to drag solder without it wicking into where I could not remove it.