Not a K1200RS, but I put a LS Superbike type handlebar conversion kit on my R1100S and was fortunate and only had to change the brake hose.
The RS is a different animal. In playing with different bars, GT & RS Comfort and various barbacks , you can get away with the RS Comfort grip and a bar back, but it is tight on both the clutch and brake line. The throttle cable is also fairly tight but workable. If I put the GT bars on the bike, I can't use a barback, cables including wiring is too short.
I've ordered a pair of hydraulic line extensions for the brake & clutch line and this winter I'll do the work to move accelerator cable and extend wiring if I have to.
So in answer to your question, " what will I have to change", you'll have to wait until you get the RT bars etc installed. It will be interesting to see how much it cost you, and then compare it to an aftermarket kit like the LS Super bike kit for the K1200RS.. Also if it was just a straight swap with the steering and ignition switch. Keep us posted.