Use Isoline Editing

If this option is enabled, all the elements of the HyperNURBS cage object — i.e. its points, edges and polygons — will be projected onto the smoothed HyperNURBS object. This allows you to select these elements directly on the smoothed object.

Although at first it may seem like you’re selecting parts of the smoothed object, it is in fact the cage elements that will be scaled, extruded and so on.