I don't believe you can re-enable the map and get anything other than a blank map; at least that's my understanding.

Can you even tell which direction you're going (NESW)? I guess you could maybe get your bearings three times a day? Sun direction at morning, at noon (by rest minutes remaining) and in the evening - yeah I'd be going around in circles most of the time as soon as I got away from the edges of things.

I suppose you could look up your seed in one of those world viewers after you're done. Would at least let you see how far off things were from what you thought while playing.

Good luck! (and better you than me lol).