* Electronic vs. Mechanical Control: The biggest hurdle. The 1996 Chevy's computer system controls shifting, torque converter lockup, and other functions in the transmission. The TH350 has none of this; it's entirely mechanical. You'd need to completely bypass the car's computer system for transmission control, which is a very complex undertaking and potentially unsafe.
* Bolt Patterns and Mounting: The bellhousing bolt pattern on the TH350 is different from the engine in your 1996 Chevy. You'd need an adapter plate, which adds complexity and may affect strength.
* Transmission Length: The physical dimensions may not be compatible with the driveshaft and transmission tunnel.
* Electrical Connections: As mentioned above, the electrical harness for the 4L60E (or similar) is incompatible. You would need extensive rewiring.
* Speedometer and Odometer: The TH350 doesn't provide a signal for the speedometer. You'd need a separate speedometer calibration device.
In short, while theoretically *possible* with extreme modifications and custom fabrication, it would be an extremely difficult, expensive, and unreliable project. It's far easier and more sensible to rebuild or replace the existing transmission with a compatible unit or even a rebuilt 4L60E.