I am not a transmission guy. I have bought a 3chd 4l60e out of a 03 Suburban. And I have no clue if it will work with my 02 z28. The new trans I bought has a black box with 2 plugs on it and the one I pulled out don't



This is the new one





This is the old one

 

The transmission itself is completely compatible with your car.
The "black box" performs the Starter interlock, tells the PCM whether you are in Park/Neutral and runs the backup lights.

Since it appears your can doesn't need it, you can ignore it or even remove it.
If the replacement trans has a longer shift shaft, you may need to improvise your shift cable or have a trans shop swap shafts for you.