The 97 Yukon (GMT400) used the 4L80E transmission. The 2000 Silverado (GMT800) came with a variety of transmissions, but mostly the 4L60E. However, it is possible to swap in the 4L80E.
* The 4L80E is a physically larger transmission than the 4L60E. This means that the transmission mount will need to be modified to fit the new transmission.
* The 4L80E has a different transmission fluid pressure system than the 4L60E. This means that the pressure sensor and solenoid body will also need to be swapped over.
* The 4L80E has a different tail housing than the 4L60E. This means the driveshaft will need to modified to fit the new transmission.
In summary, it is possible to fit the 4L80E from the 97 Yukon into the 2000 Chevy Silverado 1500, but it will require some modifications.