I am wondering if all of the specs need to be matched or are there some that don't need to be exact.
It completely depends on the application. Unfortunately you don't give us enough information to provide you with a good answer. However, in general stepper motors are fairly standardized. If you get one with the same step size, and the same general shape and size, and you can wire it up correctly (since the driver uses 4 wires it's pretty easy to convert a 6 or 8 wire to 4 wire use) then you should be fine.
If the device that uses the stepper is using it near its limits in terms of speed, torque, etc then you may have problems if you don't match the winding impedance, mechanical resonance, etc. This is only a problem in high performance machines, though.
I would contact the manufacturer, if possible, and get their recommendation. If not, try a different motor out and see if it works. Chances are good it'll be fine.
The step size is independent of the wiring - a four wire stepper at 0.9 degrees per step is the same as a 6 wire and 8 wire, just the coils have taps in them (or separated). So you will need to match the step size regardless of the wiring.