As many here have said, any practice will help you. Just make sure that it isn't just slinging rounds down range. Practicing with a .22 or air rifle is great, inexpensive practice, provided that you concentrate on the basics: trigger control, breathing, target acquisition, etc... Couple that with practice with your hunting rifles.
Dry firing is a great training tool. Set up a picture of a critter on your basement or garage wall. Practice getting your UNLOADED rifle on target and "taking the shot".
Getting your shooting ready for a safari isn't something you can "cram" for, so being proactive as you are is great and I'm sure you'll do fine when you go on safari.