That’s the point though, having both sabers would’ve made everyone more aware of the destroyed saber being used. Luke didn’t know it had been broken apart, but knew Kylo would be further angered by its use. I know a lot of people didn’t even think about the destroyed saber being the one used when they first saw the scene.
I don’t think Kylo would fall for the projection of both sabers were used. I think he’d have been more aware and suspicious. Swapping to the green makes sense, but I prefer it as is.