I've never really been able to find a fixed method to make rivers less wide. Sometimes it works if you soften the river layer several times. You can also lighten the rgb values, or make a 3 pixel wide river layer, fool around with softening and then place a 1 pixel wide river layer over that and keep the rgb value at around deepest black ...
There are many kinds of commands you can try out on rivers - smooth, soften, lighten, shrink ...
But in all cases I would suggest working on a layered file for map_c ... with separate layers for everything. A layer for white only, for ocean water only, for surf and shallows, for rivers, for lakes ... layers may seem complicated, but they allow you to experiment at will without needlessly having to redo things that you might inadvertently mess up ... and you can keep on adding layers, trying them out, turning them off to compare with other methods ....
Layers, even for map_c have lots of advantages ... for instance if you do set up a river system for the map, you can them take the river layer, copy, shrink and paste into maps H or T or the ed maps to either flatten terrain, add rgb 30 layer for mapT or add rivers to the ed-maps ...