How do I get there? Is there a quicker way then walking first around the swamp then "through" it?

You can access a short-cut to Mort'ton by doing In Search of the Myreque.

 

 

 

After completing the quest, go under the Canifis bar and search the South wall, run through the dungeon and out the farther side.

 

Then run south, climb the tree-bridge, then jump in the boat.