The Navy was a couple years ahead of you, they've already started training officers to navigate by non-electric means: http://www.npr.org/2016/02/22/467210492/u-s-navy-brings-back....

The fact that they stopped at all astonishes me. In a military context, it's certainly conceivable that a ship would take some kind of battle damage that would disable its electronic nav systems.

Middies also used to learn how to sail with canvas, did they stop that, too?