Hi, Mike!
I zapped one just like yours in my setup. I wrapped the wood in a couple of layers of that new Press and Seal wrap, and then suspended the wood handle just out of the soup with string. The wrap kept the water from getting to the good patinia of the wood. The iron part of the handle had a line across it when it was finished cleaning, but I buffed it out with a stainless scouring pad. You couldn't tell the difference, especially when it was seasoned. I seasoned it on the stove top, and it looks great.
Good luck,
Jesse