Squirrels have fuzzy tails.
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http://www.engineersedge.com/screw_threads_chart.htm has a really good chart of sizes. Sorry, I meant to put that in earlier. It's all in inches, so you'll have to either correct/convert or just go with anything under 0.125 inches (1/8 inch). Keep an eye on the 'major diameter', that's the diameter of the screw and the threads. The 'minor diameter' is the body of the screw, not counting the threads. You'll probably want to go with a #4 screw. For the brackets, you'll also want to have a head diameter closer to 5 or 6 mm. #4 screws are tiny, diameter-wise, so if you can step up to #6, it might be better. #6's can be found at your local mega-hardware store. Going deeper, there are also T-nuts that take a larger screw diameter (1/4-20 is a commonly available threading for them) that you would drill a larger diameter through-hole, put the t-nut on the back and when you screw the pieces together, the t-nut is pulled partially into the pre-drilled hole. This might be a much better way to support the two pieces of plywood. It's how I've put a lot of (non-robotic) wood together. http://www.fastenal.com/web/products.ex?now=1&N=999600087&Nty=0