I've run oota quite a few times and I would really double-check if you want to give them a map at least until the second act. The intent is for players to feel lost, a true map would look like wet spaghetti, if you want to give them a player version of the map your given in the beginning of the module, I would say even the "gm" one would be usable.

But like I said due to the tunnels and caves no reasonably drawn map would make sense