When I replaced mine, I tried to be smart and attached a string to the old cable before pulling it out the back of the chassis.
The string helped with pulling the cable into the center tunnel, but since the holes in the chassis and body were not very well aligned I never succeeded in the last part, pulling the cable end up behind the dash. After a lot of work and bad language the string snapped and I decided that I would never be able to get the cable through the holes.
So I pulled the cable out again and started it from the front instead. After a lot of wiggling and pushing the cable came far enough into the tunnel that I could reach it from the hole under the arm rest. From there it was fairly easy to push through into the engine room. It all could be done without lifting the car, but with removal of the center console.