Calculating the amount of torque needed to turn shutter
You have calculated the force required to operate the shutter but not the torque.
Assuming that the lever is perfectly horizontal and the pulley cable is perfectly vertical, you must multiply the force of 126 mN by the distance between the shutter axis and the point on the lever to which the cable is attached. For example, assuming your diagram shows the shutter displayed 1:1 on my monitor (which I'm sure it doesn't!), I measure the distance as 30mm giving a torque of 30E-3 * 12.8E-3 * 9.81 = 3.8 mNm.