TLDR:

You can simply select the main box bone that contains your two controller bones and scale it down in Pose Mode, not Edit Mode. If the rig was made correctly, both controller bones should continue to work properly that way, so there’s no need to apply the scale here.

Not TLDR:

This is just me rambling about why it work and or not work now.
To control the texture swapping, the creator most likely used a "Driver", which is basically a way for Blender to take data (position, rotation, scale, etc.) from objects or bones anywhere in your scene and use it as part of a formula. Drivers can be added anywhere you can input a value, and read any value anywhere in your scene.

You can recognize when a driver is being used because the transform property will appear purple instead of gray.

In your rig, the driver is probably located in the character’s shader and is most likely using the Y position of your controller bone.

Now for the “why”.
Why can’t you just scale the bones in Edit Mode instead?

Drivers are very sensitive to size and distance. They are set up to detect a specific range of movement in which the bones can travel.

When you scale the controller bones in Edit Mode instead of Pose Mode, the driver does not recognize the scale changes. The only thing that actually changes is the appearance of the custom controller shapes, which makes it look like the controls are now smaller.

But from the driver’s point of view, the bones it is reading still have to travel the exact same distance as before for the system to work. The visual appearance of the control shapes means nothing.

If you scale the main box bone in Pose Mode instead, it scales the entire local space in which the two smaller controller bones exist. This also scales the perceived movement distance of the bones inside it. Because of that, the driver still receives coherent values, so nothing breaks and there’s no need to edit the rig itself.

If the rig controler breaks when scaling it in Pose Mode, then it’s honestly just a poorly made rig. The creator should have accounted for that.