I'm just wondering if there are any techniques/plugins that can assist remove these over delineated edges without a manual brush approach ?
If it happens that you do not have a better version of the photo and the black edge must be taken off you can simply delete it. The next method works in this high contrast case.
make a selection which covers the statue and its black edge. You get it easily in this case with the Quick selection tool. Select the sky and invert the selection.
Copy and paste the selected area to a new layer. Apply 2 px Gaussian Blur to the selection in the background layer. It blurs the statue and its black edge to something less offensive:
- Invert the selection. Expand it 2px (=Select > Modify > Expand) and delete the edge of the copied statue:
The edge is replaced by the blurred edge+statue and it can still be seen but it's not as easily noticeable.
A more manual fix is to make the same selection (=the statue+the edge stroke) and drag the color outwards against the selection border with clone brush.
Even more easy is to select the sky, expand the selection 2px and drag with smudge brush the sky over the black stroke. It's done partially in the next example:
The lower half has cleaned edge.
I guess these options are not wanted in the question, but just in this case it would be about one minute job to do the sky stretching over the edge with the smudge brush.