Why make something complicated when it can be staggeringly simple - no sums are needed.
Erm, your method still requires a calculation, because effectively all you are doing is finding the number of degrees off runway heading. You still need to apply that figure (whether calculated or using your HSI method) to the reported wind speed to get the x-wind.
Personally, I'm with the piece of paper. Where I fly, we are load limited, and evey knot of wind makes a large difference, hence a piece of paper with both headwind and crosswind component.