You can safely substitute 358 Win loads in a M98 action.
A good rule of thumb when there is no or little published load data, is that loads for the same case, but with a smaller bore size are safe, even published max loads. In this case that applies to the 8X57.
Another rule of thumb is that loads for the same bore size, but in a larger case are not safe, at least the published max loads. In this case that applies to the 9.3x62, so if your loads got into even its min load range, you should know better.
The best bet (and splitting the difference), is if you find a cartridge a bit smaller with the same bore size. In this case, that's the 358 Win. If you are skittish about such logic, the 358 Win has an extra layer of safety in that published load data is on the low pressure side in deference to the many lever guns chambered in it.
With a 250gr bullet, do not exceed 2350 fps with the slowest usable powders (e.g. Varget). Go slower with faster powders like IMR3031.