Remember that you can use "dots" as swept section, if you use it at the end of the swept then change the "end condition" to tanget and increase it's value it will create a shape like the expected one.
I just discovered that this doesn't work anymore. I'm on ST8 and I don't know when this broke out but it is a big loss of functionality.
I'm not sure if Swept had the point capability before but in ST9 and some versions before you can select a point in the surface patch command.
This command also support a "guide curve" so you can use the curve you have in a sketch corresponding to your Elevation view in your image. (see the image attached, i'm not very clear in my explanation !)
With curvature continuous, the result is pretty good.
For the swept feature, i used the Arc lenght options so the two sides of the swept are followed until the end. I'm not sure about the exact shape of the hook though...