Surely it depends on what you're after. A .416 Rigby might be too much for dik-dik. On the other hand, the largest elephant ever was shot with a .416 Rigby, so how much bigger do you really need? It's flatter shooting than many larger calibers. It can be built on a standard Mauser 98 action, but usually isn't because the receiver ring has to be partly milled away to get the bullets past it and magazine capacity will be limited.

A lot of African PH's swear by the 9,3x62 with the right bullets and, if you're confident with it, why not? One thing I have found is that, if you're presented with a situation your brain has trouble processing, such as being charged, you tend to do things automatically as you have trained to do. So if your favourite rifle has a tang safety, that's what you'll be subconsciously pushing instead of that nice 3-position safety on your new but not as yet much used custom 40 caliber. In the few seconds you have to get this error sorted, that could be important.

A .404 with modern brass would not only do the job but would have, I presume, the same (or similar) action length as the 9,3x62 and could be fitted out in the same style on a Mauser 98 receiver. If you are going to change something basic, like action length, safety, stock style etc., get plenty of practise so it's automatic, even just mounting, dry firing and re-cocking on the shoulder. But get off to the range too and try different distances, moving targets and etc. You might consider looking for a practise bullet with much the same POI as your premium ones.