A .375 H&H will be fine. Getting softs and solids to hit the same point of impact can be tricky. Some of the ammo manufacturers are pretty good at this. It pays to buy a few different brands and do some serious range work. A 9.3x74 is not a Cape buffalo round if things get dicey.

If you load your own, Reloder 15 is a good powder for the .375 H&H when solids and softs must work together.