My opinion on the grips question, the only way to put them on the K1 and still have them operable, is to move the entire handlebar assy, wiring and all. I can't say if the actual bar is the same size(width wise) or not. RS bars are different(shorter) than LT bars, and I don't know what the K1 has, someone else may know.
Any attempt to remove the heating elements from the bar, will risk ruining them....
You may be able to remove the throttle side, as the heated element is attached to the plastic rotating throttle tube, to change out the brake master cylinder if you want to, otherwise leave it in place.