* The Blazer's original transmission: A 96 Blazer came with several different transmissions depending on the engine and trim level. A 350 (likely a small-block Chevy) would require a transmission capable of handling its torque and horsepower. A smaller engine's transmission might not be strong enough.
* The 350 engine's specifics: Even within "350" there's variability. The output shaft's size and configuration will dictate what transmission can be bolted to it.
* The transmission's bellhousing: The bellhousing is the part that connects the transmission to the engine. The bolt pattern and overall dimensions must match the 350's engine block. A 96 Blazer's bellhousing is almost certainly not compatible.
To use a 96 Blazer transmission, you'd likely need an adapter plate (if one exists), and potentially custom driveshafts. Even then, reliability would be questionable, and the overall effort might outweigh the benefits of using that specific transmission. It's far more common and reliable to source a transmission specifically designed for a 350 small-block Chevy. Common choices include the TH350, TH400, 700R4, and 4L60E (and their various variants).