With all my respect to SPYDERCO Tri-Angle Sharpmaker (really very versatile and easy to use sharpening device) no way I can consider it any good for the purpose you have mentioned. It has preset sharpening angles at 40 and 30 degrees. Sharpening your throwing knife with thick and obtuse edge in fact you will be forced to reprofile it to 40 degrees first. This means that you should grind the edge between sharpening area and blades main grind (back part of sharpening area) removing tons of steel until you will come close to very edge. Since the basic set of Sharpmaker has pretty fine hones this work could last forever. Even buying optional diamond hones you would accelerate it only slightly.
So my advice would be get cheap coarse silicon carbide whetstone, as big as possible, to do an initial reprofiling. Then finish on each fine sharpening stone or device, for ex. Sharpmaker.
Also, be prepared to poor performance of thinned edge because so-called throwing knives are usually made of pretty soft steel. It will roll easily on impacts.