Simpler solution: Calculate the volume of gas that the container will hold, then use that to calculate the volume of liquid water that could condense would be in that volume of gas, the term negligible comes to mind. I am recommending that you do the calculation not to be a jerk, but so that you will have real peace of mind, your concept is sound, but at the volumes you are talking about it should not be a problem. Don't forget to calculate for the displacement of the film.
I say toss it in the fridge, and if your really worried just leave the container open enough to allow air to get into and out of the container then seal it after it has been cold a few days and all that water is gone. You would want to put the containers in a light sealed box, or a dark bag to do this just in case.