Is the drive shutting off when making a fast move and an abrupt stop with the jog box? If so and this is a newer machine it is an added safety feature. One way to tell is if you can move the machine with a slight push without the emergency stop activated. The only way to avoid this if this is a newer machine is to make a gradual stop with jog box.
The switch has screw terminals on it, so there is no soldering. If I remember correctly you only need to remove the 4 screws on the back of the jog box and if I remember correctly, the 4 screws around the joystick. The retaining nut was glued in place. Once the glue is removed it is a straight forward process. Remove the nut, push the switch out, insert the new one, and reassemble everything.