Beautiful rifle, congratulations on a great find. Especially love that old Hensoldt in claw mounts. Don't see that too often.
I use the Hawk 200gr bullets with good success in a 1905 Mannlicher in 9x56, which is very similar to the 9x57. Accuracy is very good, even surprising for an old carbine fitted with a receiver sight. Not much experience to report on game. I've only taken one deer with the rifle, and it dropped.
You'll note on Hawk's website that they offer 9mm bullets in several diameters. This is because the actual bore diameter seems to vary quite a bit from one manufacturer to another in older 9mm rifles. The bore in my Mannlicher measures .352, so I go with the .353 diameter bullets. So it is helpful to slug the bore before ordering.
A less expensive option and potential solution to component shortages is to obtain a bullet swage die, which permits the resizing of more widely available .358 bullets. Sizing to .356 with jacketed bullets only requires only a pass through one die, which will fit in a standard press. Lee makes them, and I believe they often stock that size. I once had a Husqvarna in 9x57 that was very accurate with the resized Hornady 200gr RN. I have read accounts of some who claim that the process degrades accuracy, or facilitates jacket/core separation, though I haven't observed either issue.
