I can think of many things I'd like to do naked, but diving isn't one of them. Skydiving, maybe... 
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It was in the Persian (Arabian) Gulf. Warm water. One of the two parties involved didn't anchor their 3mm vest which floated to the surface and was retrieved by the gang on the boat. This caused a bit of embarrassment. I didn't use a wetsuit. Great fun!I'm sure that made for an interesting logbook entry. Bonus points if you were diving dry!
If I average the water temperature during all my logged dives, I seriously doubt it'll be in the double digits (C). So, no. No way in heck.
You're a gal. You think you have problems? For us guys, the embarrassment is way too much. Even before we start considering the discomfort.
Not since Coca Cola marketing decided to change it's original recipe have I seen a worse idea! I don't care if you are built like The Rock; giant stride or backroll entry is going to be way too much bad naked for some poor soul to witness. Try something classy like a nice dinner out, champagne or fine wine.
Back in the early 90s I saw a group of about 8 divers all with only BCs. I can tell you, men should not do it.