Replacing battery in Sony Walkman NWZ-A17

From a YouTube video, it seems that the replacement lithium battery for the Sony Walkman NWZ-A17 is US 383759 A9H. Can anyone share how best to find a reliable supplier for this battery? Also please share any tips on wire color. The video shows 3 wires (red/black/white), whereas some suppliers show 2 wires, and another has 3 wires, but are red/black/yellow. Do you know if the thin object taped to the battery is a temperature sensor, and is the tape type “Kapton”? The repair looks simple, but it’s for someone else and I want to see if anyone can add to what little I am finding on line or the user manual. Thank you in advance!