A little bit of basic physics: A cartridge case contains pressure. Said pressure works against the action's breech only by the base area of the cartridge case. The case works like a piston against the breech. A bigger diameter case, having a larger base area, exerts more strain on the breech at the same pressure. The length of the case or the diameter or weight of the bullet has no relevance here, as it is contained by the barrel. As the 7x57, the 8x57IS and the 9.3x62 share about the same base diameter and the same allowable pressure of 3400 bar according to international CIP rules, so they put the same strain on the action. The 9.3x64 has a max allowable working pressure of 3800bar working on a much larger base area, so it puts a much higher load on the breech. The pressure is only increased by about 10%, but it works against a much larger base area too, so the load it puts on the action is increased by about 25%. Another example: The .223 Rem has a pressure of 3700bar, the .416 Rigby only 2850bar, but the Rigby has several times the base area that makes the pressure work against the breech, so the load applied by the Rigby case is much higher than that of the .223.
This is the reason why I would put the 9.3x62 in any action suitable for the 7x57 or 8x57IS, but not cartridges of higher pressure and/or larger base diameters. Otto Bock designed the 9.3x62 this way in 1905!