Since 89 to 96 swaps across the 94.5 line for the transfer case input gear helical pitch *and* the 95 to 96 transfer case tailcone seal style change, you're going to have to swap in the AW4, transfer case, AND rear driveshaft... but AX15 vs AW4 have different driveshafts, so you're going to need to find an 87-95 4.0/auto/4wd rear driveshaft from a donor with the same rearend as you, and a front driveshaft from any 4.0/auto donor. I really wouldn't do this swap, it's opening a pretty big can of worms mechanically. You will also need the transmission crossmember and AW4 shifter + cables from the donor, possibly a TV kickdown cable from a 91-01 AW4 (not sure if the RENIX style TV cable connects to the throttle body on a 91+ the same way or not), and I'm sure I'm forgetting some other stuff. Oh yeah, trans cooler hoses as well.
The electronics are going to be interesting, you will want to find a 91-96 TCU and wire it in, since your TPS is the OBD style the 89 one may or may not work. It will involve a lot of splicing since your harness doesn't have any of the connectors for the TCU, might be missing contacts in the brake light switch, doesn't have the wiring for the TPS to TCU connection, the NSS, the trans sensor+solenoid harness, etc.
If you can find a 91-96 donor with 4.0/auto/4wd/same rearend as you, the swap will be much easier (you'll need trans, transfercase, driveshafts, and support parts for the trans), but will still involve a decent amount of wire splicing.
I would really just try and beg/borrow/trade another AX15 off someone, or rebuild yours. What's wrong with it? If it is just the synchros you can get all the ones you need off quadratec for around 100 dollars and maybe throw in some bearings for another hundred or so. I haven't ever rebuilt an AX15 but am hoping to pick up a spare to rebuild soon.