I would assume that the bird has to be from First of the Sun, as per this WoB:
It's lucky enough that a bird from a totally different environment, totally different place, would have similar enough gut flora for Sak to work- the birds on the mainland and the ones on Patji must of had common ancestors at some point. I would find it incredibly unlikely that a bird from any other planet (even a bird from somewhere distant on First of the Sun may not be able to become Aviar, I'd think) would have compatible gut flora to this incredibly specific, unique, isolated, magical system by happenstance.
Which would also mean a no to the Aviar axehound, unfortunately. Hope this helps!