I downloaded the SVG and noticed: The oceans are masked with the back shape that does not allow path operations. The following succeeded:
- hiding the latitudes and longitudes away
- changing the land areas to single solid color
- filling with paint bucket the land areas to get them as Inkscape paths
- adding stroke to the land areas
- removing possible unwanted stroke sections
- making the stroke to path (=coastline path)
- subtracting the land areas from the coastline path
- coloring the rest of the coastline path to black
Here's a screenshot of the partially filled land areas (=orange) and all path nodes visible:
Here's tested to make the coastline path. The land areas are just subtracted, so the coastline path is only on the sea. No part in the edge and lakes is removed, small islands were skipped
No need to paint the land areas. As well you can paint the oceans. The coastline path on the sea is achieved by making an intersection with the full coastline path and strokeless sea area.
Here's another fill example. Atlantic and Pacific areas were filled with red and got black strokes. Then an union was made as path operation:
The path was duplicated, stroke was removed from upper copy, fill from lower copy, the stroke was converted to a path (=the full coastline path) and the strokeless ocean was intesected with the coastline path. No tinkering with islands were needed:
The black strokes at the edges are probably unwanted. They should be removed just before conversion to path. Selection of multiple stroke segments for conversion is easy in objects panel or as well by the same color in Edit menu.
To keep all placed properly have a hidden copies of the original shapes. Finally you want only to take the coastline path and place it under the latitudes and longitudes in the object panel.
Stop press and at least upvoting! The result is good onscreen, but high zoom reveals the inaccuracy. Paint bucket doesn't create complex enough path for this!