Do you have more from the cobra other than the engine and trans?
Your project certainly is doable, but you will need a lot more parts than you currently have, including many fox specific parts that don't come on the 4cyl. Wiring needs to match up to the year of the car, the transmission, and the ECU, so you will be hunting down parts.
Ideally, it would be MUCH easier to do the swap if it was done on a 5.0 fox roller. Being as you have a 2.3L roller, you almost need to pick up a 5.0 parts car of similar year to the 4-cyl car to take what you need.
The SN95 harness is a bit different in the dash wiring, the lights, air bags, etc. It's far more complex to use vs using a fox v8 harness, or even a painless wiring harness (although I've heard plenty of issues when using these too)
You'll need to convert the cobra motor to a fox motor as well. Accessory setup, 93 cobra upper and fox style throttle body. Shorter fox bellhousing and input shaft, etc. Double hump X member, etc etc.
Again, not an impossible swap, but you'll need to chase down a lot of parts and wiring and such