99 V6 in a 96?

The motor will drop right in. There are a few things that you should think about tho. 99+ motors use a returnless fuel system, and your 96 uses a return style. You will have to do some modifications to the fuel system, you could just delete the return line and you will have to put a fuel pump from a 99+ in it. If you use the 96 pump in there you will burn it up in a hurry, its designed to run constantly and any unused fuel goes to the return line. The 99+ pump pulse at fuels demand.
It would also be good to get a tuner and a proper tune for the car. As far as any other things i really can think of any off the top of my head.

Ok, I may be wrong on this has my area is actually with the GT. However, in 1999, the Mustang was reworked. With major changes in the wiring, electronic dash, COP, re-worked fuse panels, and other changes.

The OP did state they were interested in a "NO MOD" installation. To me, that rules out using the PCM and other electronics from the 99 because of differences in the body wiring harness. The differences in the fuel system has already been mentioned.

I would think that if the 96's PCM, fuel system, wiring, spark were all retained, the swap would be straight forward. Of course this would mean transferring all of the wiring and such from the old motor to the new.