It is impossible to replace the home button assembly and preserve Touch ID function. The sensor is designed to be secure and it is uniquely paired with each CPU. You can't extract the key from the sensor or the CPU because they are designed to take the key to their graves. Reprogramming them is unlikely—even for Apple. They have never offered to replace the button and likely never will. (Update: They do now.)

So if the device is under warranty, leave it to Apple. If the sensor is replaced by you or damaged, you will lose Touch ID forever.