Apple - How can I prove to an airline that the iPad mini they found is the one I left on the plane, without giving them the passcode?

If you have your iPad's serial number it should be visible on the back of the device.

source: Apple

As mentioned in the comments below, you can get the serial number by either:

• Logging into the AppleID associated with the device at appleid.apple.com.
• In the Apple ID area in the Settings app on your iPhone logged into the same Apple ID. (The very first thing if you scroll to the top of Settings.)

Tell them that you are uncomfortable providing your passcode to another person, but you would be happy to unlock it in front of their staff at the airport when you retrieve it.

This does require you to travel to the nearest airport, but it is a reasonable compromise that protects both interests.

Describe the lock screen background picture, especially if you have a custom photo or image.