First off, nice little map. I like the layout. It'd look great colored in a watercolor style.

Use this image as a layer set on Multiply and then paint on layers that you add underneath. The lines will show on top of whatever you draw and your original artwork will stay intact. You can try other blending modes as well if you want but Multiply is the one I use most. Hopefully you're okay with keeping the grid, though, because I reckon that'd be hard to remove without destroying the drawing.

Hope that helps.
M