How to secure wire fished between two plastic switch boxes

I have two light switches in two separate plastic switch boxes. The upper box controls the motor of a fan, and the bottom switch controls some outlets. I want to change the wiring so that the bottom switch controls the light on the fan.

Since the wiring for the fan came into the upper box, I plan to fish new wire from the light in the upper box to the lower box, and connect that to the lower switch.

However, this post says that the new wire must be clamped to the switch box, since it is nonmetallic. Unlike the box in that question, my switch box does not have clamps, and looks like this:

How can I secure the wiring to the switch box?

Edit: Just to be clear, the switch boxes are already in the wall and are connected as described above. I am just trying to modify the wiring. I would rather not remove or replace the boxes if possible.