Yes you can swap out the motor.
No you do not have to do anything OBDII to it. You will change a few things to make it OBDII.
What you will need to swap from your motor to the 96 to make it OBDI are the following ...
- S13 distributor
- S13 coil
- exhaust manifold
- intake manifold
and if you have the time to do the upgrade for the S14 motor ...
- S13 DE cams
It'll be easy since you already have these in your car now.
Either than that everything is plug and play. You will have 1 or 2 plugs that might not be used but don't worry, you're good.
I also have an early 95 motor in my 89 S13 which was still OBDI (1991 - 1995.0 = OBDI | 1995.5 - 1998 = OBDII). Motor has been running fine and with a few bolt ons and tuning, car is running mid 14's all motor.
As for the sleepy eyes, do a search. There is an under $5 poor mans way of doing it.