I don't think the problem is with your 4 channel Skysport buddy box - it's with the HiTech Optic's trainer system. On my Futaba 9C system it's trainer system can be set up to pass down all the mixes and programming on the master radio to the slave or training radio.

Quoted from the 9C user's manual - Trainer system includes the “functional” (FUNC) setting, which allows the student to use the 9C super’s mixing, helicopter, and other programming functions even with a 4-channel buddy box. (Optional trainer cord required.)