Is any user data stored on Apple AirPort Express
Your AirPort Express does store some unique data including your wireless passphrase, routing table, ARP table, etc.

Beyond that, there should not be any personal data on the device. It does not cache files.

Nonetheless, you should open AirPort Utility on your Mac, select the symbol of the device, and select Base Station -> Restore Default Settings… from the menu bar. That way, the next user will start with a fresh configuration.