The battery usually puff up because of internal gas discharge. I have no idea what gas they may be, but it’s just gas. To reduce the volume of gas, you can either use high pressure or low temperature; the former is harder, but the latter may be worth a try: I just opened a lightly puffed iPod nano 4th gen (the “wet mark” showing the screen contacting the glass panel was only about the size of a grain of rice) by freezing it in a conventional fridge (no idea the actual temp, maybe 0 F or -18 C). I used a sealed container with some desiccant for it; there should be very little chance of things going wrong.
Notice that if you work in a humid area, condensation may form on the iPod inside and out: make sure they are off and discharge the battery if needed. Once you get the screen off, everything else should be very straightforward. Make sure to let the iPod warm up to room temperature before pulling out the solder iron or trying to start it.
Hope this helps.
(P.S. I did damage the screen mounting hardware a bit before trying the cold method because I was too optimistic about the battery expansion… the display retainer pulled off and the screen metal bracket is bent. The battery also didn’t give up without a minor hassle, so be more careful than I was.