I would not cut it down. I have snapped stems bigger than what you have and they survive just fine.

Take some heavy tape, such as duct tape or better yet aluminum tape if you have it, and wrap a piece around where the break is/was in such a way that it will support the weight of the cola, and let nature take its course, it will hardly affect anything as far as life is concerned. It will form a knot around its injury and just make it stronger.

good luck