The announcement on the PA speakers for Popeye states you must have shoes on. I do what was mentioned up above. I take off my shoes and socks in the queue, then walk into the ride wearing only my shoes (no socks). I sit down, buckle my seat belt, then put my shoes, socks, and shirt into the middle compartment. It's really a formality, the ride ops know everyone is taking off their shoes, but they look the other way once you have the seat belt buckled. If everyone gets the belt buckled first, then the ride op will take a quick look, and walk away. Agree, ponchos don't help, you get soaked because the water comes in from the sides.
I usually bring two pair of shoes on my trips. One for going on the water rides in the morning (my old pair), and another for walking around in the afternoon (my new pair).