I fish the Tortugas and keep fish for 2 days before cleaning them. I take the fish off the hook and toss it in the coller of ice while he's still floppin. We spend 2 nights on the water and head back to captivity to clean our fish, grouper, snapper, cobia, kings, dolphin, and whatever else we catch. Never have been sick after eating any of our catch.
I've kept Snook out of the water and ice for 2-3 hours before cleaning them, but it was cool weather and at night.
I suggest gutting your fish first, toss it in the fridge for a day or two and you'll be perfectly fine.