For this a bought an IWISS IWS-3220M crimping tool from Aliexpress as cheap alternative to the official crimper. Given the small size of the SH connector I recommend buying plenty  of the SH contact (SSH-003T-P0.2-H), I bought 100 and got through a quarter of them before I had mastered the art of crimping. Instructions come with the tool and very detailed  steps and pictures can be found in the official documentation from JST (CHM-1-2146).

1. Strip ~5mm of insulation from the 32AWG wire (smallest size compatible with SH contacts), then twist and cut the conductor to ~1.25mm.
2. Close up the crimping tool so that a gap remains for insertion of the contact. From the back (side with no writing) insert the contact into the 1mm slot in the crimping tool. Make sure the front of the contact is aligned with the front of the tool. Insert the wire from the front, I used a finger nail about 1.25mm back from the conductor to control the insertion depth. Slowly completely close the tool.
3. Check the crimp under a microscope to make sure it is consistent with the pictures in the JST guide.
4. With a small pair of pliers very gently squeeze the two parts of the crimp, to make sure they are narrow enough to slide into the plug with only minimal resistence.
5. Verify that the crimped contact can be inserted into the plug, without sliding it until it locks.
6. Put the wires with attached connectors to one side, next step is to thread them through the square PVC tube.