The map is not literal
First of all, I'd make this map indestructible. It certainly can be damaged - but exclusively by magical means, like rituals, that would eventually guarantee that it will eventually "heal".
Then, I'd say that only a specific kind of magic ink can be used to draw in this map. Either this or make it so that changes to the map can only be done during a given ritual. Anything else, like a pencil or regular ink won`t work (maybe the ink and the graphite just fade, eventually).
This magical map works by projecting the idea of the drawer in the terrain - but it won't always work exactly as it's supposed to. For simple things like drawing a tree, it might work perfectly. But when a greater change is done, the effects on the terrain start to get more and more unpredictable.
So if you draw a tree in the middle of a square, the ink will slowly spread, over the course of days, months, years - decades or centuries even - and slowly change its form and colours to start becoming a tree. It will, most times, be the tree the drawer thought of. But sometimes, the tree might end up becoming a different tree (which is of little consequence).
This way you don't really need a person that knows how to draw, since the map kind of "scans" the drawer's idea from his mind. Just imagine how silly your map would be when found by your heroes, after 3000 years of people drawing shitty sticks and weird shapes in it.
You might also adapt this to fit the extreme versions of what can be done to the map. If you burn it, maybe a great fire strikes the affected area. The burn stain would also change, just like the magic ink, and eventually portrait the destroyed area. The same can be said of tearing the map. Maybe it glues itself back together while portraying the huge canyon formed after the greatest earthquake ever registered.
These unorthodox ways of using the map could be even more unpredictable. We'd all assume that burning the map would mean a great fire. But why couldn't the affected area just become a huge tar pit or a swamp over hundreds of years? - a drastic change to a biome. This factor of randomness could be a way to ensure that the map is not a weapon of mass destruction - at least not that easily.
Remember that: These more agressive ways of shaping the map must also be done under a ritual, to explain why it heals itself even if heavily damaged (it's a magical map, dude :P)