Frog Song is incredibly powerful. So powerful that Nagato lost control completely of all his paths affected by it. He had to send out the final 3 because first 3 were completely incapacitated.
Genjutsu attacks the nervous system and it affects your 5 senses. A Genjutsu can't work on something with no nervous system, like a rock, a chair, or any inanimate thing. The Peins are all dead bodies. They have no nervous system, no heart beat, and are inanimate. The only reason they move is because of Nagatos black rods in all areas of their body. It allows him to control them as he pleases. Now with that said, Genjutsu attacks the nervous system, yet the Peins have none and were still affected by Frog Sound. Why? Frog Sound should have had no affect on them yet it did. Shark Skin giving Kisame chakra will not work because that is simply Chakra Dissipation. Nagato is already constantly transferring his chakra into the Peins body for them to move. If that were the case Frog Sound would not have worked on them altogether because it would have been instantly broken. Shark Skin giving him chakra won't change anything because Nagato was already giving his Peins chakra and nothing changed. The Rinnegan was helpless to Frog Sound, it is of such a high level that it can affect things with no nervous system and thats going beyond all genjutsu we know of.