How much extra drag does an external HF antenna incur?
As this film shows with brilliant simpliciy, the drag of a round wire is almost 10 times the drag of the same thickness streamlined shape. 

Biplanes use streamline rod for flying and landing wires because of this.  There is enough flying/landing wire on a biplane for it to make a huge difference.

On a long antenna wire however, there really isn't a practical way to streamline it, and even if you did, to keep the streamline contour properly oriented, so you just live with the drag penalty of the wire.  

It also helps that the sharply "swept" angle of the wire in the picture to the airflow means the profile presented to the airstream is more of an oval shape than circular, so the drag of the swept wire will be somewhat less than a wire presented to the airstream at 90 degrees.

So in the case of the 737, the wire itself is probably pretty minor factor overall, but I wouldn't be surprised if the wire costs a couple of knots of cruise speed at a given power setting.