I'd avoid soldering if at all possible. Do it the way it was designed to be done. There is a heck of a lot of IDC connections in the world where reliability is important. Proper specifications would be nice, but...
If it was me - I'd go for a wire with a solid conductor that won't pass between the two prongs of the connector without spreading them - just a little (not too far or they'll splay outwards). This will put pressure between the connector and the conductor, maintaining a good contact. Alternatively, a stranded wire where the bunch of strands needs to be flattened a bit to fit between the prongs.
Either way, the insulation of the wire needs to big enough to get caught on the barbs on the connector body - but not so big that they spill out past the slight rectangular depression you can just see below the barbs, otherwise the insulation will get pushed away from the connector body and the barbs won't engage properly.