Do the secondary bottles for Rescue™ have to be opaque?

No, they do not. Rescue™ contains ingredients that help to prevent the hydrogen peroxide's reaction with exposure to air or light.

Rescue™ Disinfectants are based on a patented technology called Accelerated Hydrogen Peroxide® (AHP®). This technology contains stabilizing agents that prevent the hydrogen peroxide from reacting to exposure to air or light, meaning that Rescue™ never has to be stored in an opaque bottle to protect it's stability and efficacy.

You may also find these resources useful:

Video: What is AHP®? What are the Ingredients in Rescue™