You can swap the whole engine with some trivial changes. The basic rule is that the electronics and fuel plumbing need to be the same year as the car in order for all of the parts to work, so in your specific scenario you will need to put the 91 sensors, ignition, injectors and fuel rail parts on the 96 engine, so that the computer and fuel pump and all that jazz will work as expected.
The other significant difference between 91 and 96 is that the later years had a different power steering bracket, pump, and belt tensioner setup, all of which bolted to the intake manifold a little differently. If you want to keep this stuff simple just keep the 91 setup, but if you want to switch on the new-style pump and tensioner you may need to swap intake manifolds (good time for a 99 since it is the same bolt pattern as the 96).
So basically pull the 91 engine out, drop the 96 engine in, put the 91 sensors, ignition, and fuel parts onto the 96 donor, and optionally replace the power steering assembly and intake manifold. There should not be any other issues