For sure on looking for a similar battery, looked at the Xperia batteries, but the nwz-z's have a 3 pin connector running from the battery via 3 short wires, there must be another device that uses this type of connector, but yet to find it, another possibility is running the walkman from a DC power adaptor, but obviously this might compromise the portability somewhat.
To get the back off the walkman, just prise off the small plastic strip with the code number on it at the bottom of the back cover, there are two small screws underneath, unscrew these with a jewellers screwdriver and carefully lift off the back, the battery is held in by a plastic cover, remove the screws on this and the battery lifts out, carefull nmot to lose the volume control plastic bit, this will be loose now..