Are the cruise control and air conditioning parts compatible?
The air conditioning should be - I'm not sure about the cruise control. But: Instead of having random Internet folks like us tell you what we think, you can easily check definitively against any of the many online parts databases. So since I'm not sure about cruise control let me walk you through how I'd find out:
1. I go to toyotapartsdeal.com (many other options, but this is my go-to).
2. I configure a vehicle (in this case, the 1994 Corolla) for parts search
3. I scroll down to Electrical and select "Cruise Control"
4. Knowing that the electronics are most likely to NOT be a fit (OBD-I vs OBD-II) I select the cruise control computer. Part number is 88240-12160. Looks like it only fits production date 09/1992-08/1995
5. Let's check the actuator too. Part number is 88200-12120, and production dates the same. Not looking so good, but let's hold off on drawing conclusions.
6. Now let's look up 1996, so reconfigure the vehicle you're searching for parts for.
7. Actuator? Yay, it's the same part number 88200-12120. So we're good on the actuator..
8. Computer? Looks like there are two options, depending on production date (remember, 1996 models were starting production in 1995).
a) For 09/1992-08/1995 it's 88200-12120 (i.e. the same as the 1994)
b) For 8/1995 onwards it's 88240-12170...
If I recall 8/1995 was the cutoff for OBD-I so that would explain why there's a new cruise control computer as well, to communicate with the new OBD-II based ECU.
You can replicate the same type of search for other parts to get definitive answers and not have to rely on hearsay.