Zimbabwe is one of the easiest countries to import hunting equipment temporary into the country as it only requires that an application form be done and submitted to National Parks. The rifles will need to be transported in a secure case. It is advisable to transport your ammunition and rifle bolt separately to the rest of the gun. There have been rare cases of the bolt been stolen in some airports in Africa during transits. The other option is to rent a rifle from the professional guide or camp operator in Zimbabwe.
See the attached letter on traveling with firearms into Zimbabwe, write in the required information and show it to customs when entering the country. The customs officials will check the serial numbers, etc.