Head size is the same (within manufacturing tolerances) and the length of the case is within a millimeter. So rebarreling or reboring would be fairly straightforward. The only difficulty I can imagine is the shape of the 9.3mm bullets. Most likely, the bullets would move through the action without comment, but even so, a rather minor amount of fitting should settle things out.
May I point out the 9.3x62mm is the European answer to the .35 Whelen. The 9.3mm uses a heavier bullet and is slightly larger in diameter. Ammo is much more costly or requires reloading.