M0 (Stop) or M1 (Optional Stop) is the normal way it is done. Not sure if Fanuc has a M6 (Tool change) code format for a manual tool change.
So:
G0 [Z+ move] (for clearance)
M0 (manually change tool)
G0 [Z- move] (back to working height)
But you may have to tell the program what new tool number is so that it applies the offsets correctly. Not sure how to do this.
I would fix the tool changer.