Ok, this is rather simple if your only using the nunchuck and not the nunchuck + remote. The nunchuck communicates to the remote via I2C, or to SDA & SDC on the arduino. If you want to reuse the nunchuck, there is an adapter that you can buy on ebay (very cheap), or you can simply cut the cable and use your own wires. (If you plan on cutting the cable, make sure your wiring is correct before soldering)
So far the smallest arduinos are the micro, the nano, and the mini/pro, all of which should work. You just need to wire it up correctly and find a way to power both the arduino and the servos. The arduinos have a suggested range of voltages to supply to them, so check out the spec sheet, and the servos usually will need 6V, so you will need to use either an AC adapter or batteries. Now being that you are going to put it inside a metal container, I suggest you tape up the bottom so that nothing shorts out.