I guess it would cost the wood + your time for putting a crate together. I trust by living in Lesotho some time you'll know how to get a few pieces of wood together..
Then the paper work in Egypt x3, aouch. I assume between 100 and 200 USD each incl -- if lucky -- back-shish, etc, etc, etc, and there many etc.. port handing for the crate, insurance, about 100 USD max, and shipping, this is the cheap part. You have to factor in handing port fees at destination as well. Some countries have a terrible reputation.
The only trouble here is the choice of destination. On some it is easy for forwarders to group stuff from different customers and load a container all together then split the cost++ more or less, but on some other destinations, this becomes more difficult, hence delays are encountered while the container is filled, not a terrible situation if you are not waiting for your bike at the other end, but still, it takes time, one may count in weeks if not months. In my case I eventually decided to cover for a container on my own to carry stuff abroad because I needed it.
My advise, just ride up to Egypt and find a way when you get here, use your McGiver's skills and get on with it. You'll find a trusty and reliable HUBBER friend on this forum who will help you if you need, but hey man, after crossing the continent and having dealt with some more important practical problems, this will become the easiest part.. Ride on!