Unfortunately there is no easy way to implement decreasing the border width via a single keystroke, but if you really need to know where those rivers are you can do the following:
Attached to this post you will find a zip-archive containing a png-file called "border_gradient.png" with narrowed borders, to copy into the following folder (after unpacking of course) :
CTGW/Data/Graphics/hexes
overwrite the old "border_gradient.png" file (but make a copy first to revert to the old style).
Ingame-preview of narrowed borders:

If you need the borders even thinner just say so.
Cheers!
