To protect the watch, wrap it loosely in a thin scrap of cotton cloth (a handkerchief works well). Then place it on a layer of silica gel (used for drying flowers - available in craft stores) and add a layer of silica gel on top. Leave it for a day or two and all moisture will be absorbed.
You need to take off the back of the watch (either screw or pry off) then remove the inner workings, if possible. Place everything under a lamp so the heat evaporates all moisture. Leave as long as needed. If you don't open the watch up, the moisture will rust the inner workings. Hope this helps. I actually do this at work as I work in a jewellery shop.
Not sure if this will work but... I know that if you drop your cell phone in water and put it in a jar of rice (uncooked), the rice draws the moisture out of the phone. I've done it and it worked. You might try it with your watch.
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