I have study the CIP measurments for the 9x57 and the 9x56 extensive and would not hesitate to shot 9x56 in a 9x57.
the greatest problem the other way is the one mm longer case, maybe.
in spring I was biding on a M 1905 and was close but dont get it in the end. was thinking if the Mannlicher becoming mine I would cut all my 9x57 mauser brass back to 56mm and try to make a 9mm Mauser/Mannlicher Schönauer round to make ammo supply easy.
do you try to load a original 9x57 into the Mannlicher xausa???

"Since I have both a 9X57 Mauser (Model S Sporter) and a 9X56 Mannlicher Schoenauer (Model 1905 carbine) I have to be careful and not get the ammunition mixed up, especially since none of it is correctly headstamped. However, since I form the Mauser cartridges from 8X57S brass and the Mannlicher version from .35 Whelen brass (which happens to have the Mannlicher .464" head diameter, instead of the .467" of the Mauser), I do have that mark of identification to work with. "

do you wish to complicate this situation further? buy a Husqvarna in 9,3x57

I make 9x57 and 9,3x57 by the same brass - 8x57IS - and distinguish them only by the bullet