In option 1, Cockroach, the skin is not a respiratory organ. Cockroaches have a respiratory system consisting of tubes called tracheae, which allow oxygen to enter and carbon dioxide to exit the body.

In option 2, Frog, the skin is indeed a respiratory organ. Frogs have a unique ability to breathe through their skin by a process called cutaneous respiration. Oxygen from the surrounding water or air diffuses through the moist and permeable skin into blood vessels, while carbon dioxide is released in the opposite direction. This skin respiration is especially important for frogs when they are underwater or in environments with low oxygen levels.

In option 3, Shark, the skin is not a respiratory organ. Sharks have gills for respiration, similar to other fish species. They extract oxygen from the water through their gills, with special structures called gill slits.

In option 4, Whale, the skin is not a respiratory organ. Whales are mammals and breathe through blowholes on top of their heads. They have lungs for respiration, similar to humans.

Therefore, the correct answer is option 2, Frog, as its skin serves as a respiratory organ through cutaneous respiration.