Map is a nice idea, but im dosent like the arrow idea, which is clumsy and quite slow me thinks (you can do keep that throught).
But instead or as a alternative, why not just do a single click on a area on the map you want see? In that why, you still will got a keyboard free game.
Im also thinks, now you have so big a map, do a auto save function when the user quit, and auto resume when the user launch the game again. Im not sure all players will do that in one run.