The JST SH connector family series is described as a "wire to board" family, and the the male pins connector you picture is is intended for surface mounting to a board.
It is not clear that a "free hanging" male pins connector housing exists in this family in the way that they do for some others - for example, free hanging contacts of both genders are relatively well known in the slightly larger 1.25mm Molex picoblade family, and get used a lot as battery connectors for tiny flying toys. Beware that even if you find the parts for a free hanging micro connector, doing crimps at this tiny scale will be challenging with a universal crimper, while the designed tool could well cost between several hundred and over a thousand dollars.
You could attempt to solder extremely fine wires to the surface mount contact tails visible in your picture, cover them with tiny heatshrink, etc, but this is likely to be extremely challenging and fragile - you'll need a soldering microscope, and a fair amount of luck and skill to get it done without melting the contacts out of position in the housing.
Realistically, just cut off the connector and splice on something more suitable. If you just want to test the fan you can poke a couple of wire wrap wires in there, but that's likely to come apart, so only do it with a power supply that can tolerate a short circuit.