I'm not sure if an iPod battery will work. It's possible. Rumour has it that one of the iPod batteries worked in the original Clip, so maybe Sansa hasn't changed the battery and you could get lucky. Unfortunately, if you find a battery, you'll need to solder it in place, as the Clip Zip wasn't designed for battery replacement and the battery is soldered to the mainboard.
If the case on the Zip follows earlier Clip designs, you should be able to (gently!) pop it open with a guitar pick or a nylon opening tool along the case seam. The battery should be just behind the clip.
Please understand this is all speculation based on previous Clip models--I'd rather not open my Clip Zip just yet!