To begin, untie the band, and lay the watch out flat in a dry, well-ventilated spot, to allow any moisture in the watch band to dry up completely. You can place it under a fan, or on a table set under an air conditioner. Wait until the band is completely dry, and then separate the watch body from the bands. However, if this is not possible, you can proceed with the watch as it is.
Next, spread a sheet of newspaper out onto a flat surface, and place the watch on this. Sprinkle generous amounts of baking soda onto both sides of the watch band, and then flip it over and repeat on the outside of the band. Some of the baking soda will fall off the band and onto the newspaper – do not blow this off.
Once this is done, bring the corners of the newspaper together, and wrap the watch up inside – you can either scrunch it all together, wrap it all up neatly from all four corners, or fold one side over the watch, then bring the ends in towards the watch, and roll it all up like a burrito.
After the watch is securely wrapped up inside the newspaper with the baking soda, proceed to give the whole package a couple of gentle shakes, to make sure the baking soda is distributed evenly all over the watch. Then, put the package aside overnight.
The next day, open it up, and take the watch out – the odor should now have vanished completely. Shake the watch a bit to get rid of any excess baking soda, and wipe it clean with a soft cloth. If any stubborn bits of baking soda continue to adhere to the band, you can use a hair dryer or a can of compressed air to blow them off.