Yep. Very simple really.

Take the final image which should really be a jpg file now. Open that up in Gimp. Now you want to use the colour select too, with a relatively high threshold - I used the following settings:
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Now click on any white area, and you should get all the white areas selected. The threshold setting will determine how close the selected area is to the white/blue boundary.

Now create a new layer to play with. This should be transparent as before. We want to fuzz up the lines a bit. So go to Select->Distort... Now in this box I used the following settings:
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After running this filter, you'll get a slightly fuzzy version of your previous outline. Now, fill this with white (if white is the background colour still, this is as easy as pressing ctrl-.) and your map will now look something like this:
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How's that for you?

Obviously you can also fuzz the blue into the white areas. To do this, go to Select->Invert Selection (or ctrl-I). Then flood fill with our nice cyan colour (if cyan is still the foreground colour, this is just ctrl-,). I found that this was a bit too distressed so left that out of the above.