If I had ice extraction picks it would be very likely I wouldn't carry them in my hands while on the water. I'd either forget or not bother.

Ski poles work just as good and make good walking sticks. Just remember to unstrap them from your hands so you can choke up near the bottom to use them as picks.

Around here the ice isn't thin for long. When somebody I know is referring to 'thin ice' that usually means it's too thin to drive on.