Hi! Solving the maze yourself is a great challenge! I remember spending a whole day on it. :D
Having that said, the route presented there is almost optimal. You can save a bit by entering the dungeon closer to Carlin here: https://tibiamaps.io/map#32490,31699,7:2
Regarding the main question, there is only one path starting from the snakes spawn here:
You can reach this place in multiple ways: longer and mostly redundant. If you allow walking over the same tiles, then even infinite ways :). This is because many of the rope spots are one-way only. You can learn about it beforehand by "looking" at the hole/rope spot. For instance, one-way-up will mention a "narrow hole in the ceiling".
I'll try to provide an example path in a few days and update the answer.