Not practicing from sticks before arriving in Africa (or Europe or South America for that matter) is one of the most foolish things a client can do. It also seems to be a remarkably common occurrence. While duplicating one's intended hunting rifle is probably ideal, I do not think it is at all necessary. What is necessary is to become comfortable quickly settling into firing position and getting the shot off accurately regardless of the rifle in hand. That can be done with a .22, .223. .270, or the intended DG caliber. In fact, with rental rifles becoming ever more common regardless of destination, becoming comfortable with the basics regardless of firearm is actually probably a useful approach.
As others have noted, do not under estimate the value of dry firing your primary rifle. Most bolt actions do not require a dummy round unless the sight of it flying through the air inspires the soul. Always use a spring loaded primer dummy round with a double. It takes a lot of self discipline to effectively dry fire. A mental tool that I use whether on the range or in the gun room is to call the shot. If it is a technique you have not used, it is amazing how accurate you can become with regard to the impact point. It also tends to encourage follow through which is, I believe, hugely important in the field.