Think of your 95 as a 91-94 1st gen Ex with a much simpler system.
95 - engine is OBDI Trans is OBDII
96 - engine & Trans is OBDII
Square peg and a round hole. They just don't work together without major work. You have to treat this swap like a 2nd gen 5.0L into a first gen.
Just swapping the ECM is not going to be enough. Your losing some circuit continuity.
That being said, you might have to replace the 96 engine harness with the old 95 harness completely, including keeping the 95 ECM. You got the short end of the stick with the 95. Your also going to run into problems with some wiring connectors on the engine parts, as they have different pin outs then the OBDI connectors.
If you decide to keep the 96 engine harness, you have to commit to converting the entire system over to OBDII.
My advise is to stay with the 95 system, and just swap out the harness, and some top end of the engine, using the 95 parts for wiring connectors matching for the 96 engine.