Because your not taking a rifle you should easily be able to pack everything in your carry on luggage. Wear a set of hunting clothes on the plane and pack two more sets and you'll have more than enough clothes for the safari. Remember you get two carry-on items, so make good use of both of them. If you plan on bringing a knife you'll need a small check bag as well and the extra space in that bag will enable you to bring a few souvenirs home.
I highly recommend you use a good Safari vest, wear it on the plane and load the pockets with all the small items you plan on taking to the field, its a great way to save space in your bags and the airlines don't count it as luggage. It also eliminates the need for a back pack in the field. Your PH will glide thru the thorns of the bushveld like water running out of a tap, you on the other hand will get poked, snagged and hung up on every tree, bush and shrub you walk past (even the grass over their grabs you), a back pack is just one more thing for those thorns to grab.
The other item I would recommend is a power converter, you may not need it but it guarantees you can charge all of your electronic devices. I would leave the mid size camera at home, your cell phone and an SLR with 200 or 300mm zoom is all you really need.
Binos are a personal choice, on my last safari my PH preferred I not use them unless we where in the truck or sitting at a water hole, most of us don't have the skill to judge African game and because you are following two or three steps behind your PH you won't be able to see the same things he does. Its more important to get on the shooting sticks quickly and then find the game you PH has spotted thru your scope, than it is to help him glass for game on a stalk.
Have a great time on your Safari.