I used a 1915-vintage Winchester Model 1895 in .35 WCF to take a bonafide B&C record book black bear a few years ago. We did spot & stalk on horseback (no dogs) so getting a bear that big was a nice surprise. One of the most fun hunts I've been on.

The 35 WCF is essentially a 405 Winchester necked down for 250-grain 0.358 bullets at 2,200 fps. Though I don't know the ballistics of your 9.3x57 above, I suspect they would be very similar.