I've searched southern silithus and ahn'qiraj, but I can see no posts for a method for getting to southern silithus with nothing but a mount. Remember to watch your health since there's no slow fall in this method and doing so could put you off course at points.
I'm borrowing part of rmoore08's post as it is the same up until a point. Scroll past the quote to see the new method.
Ok this white line is ridiculous, just go in a straight line ahead to the next pictureStart in Tanaris and go to the ocean on the east and follow it down around that southern peninsula to where the X is.
Here is where you will start. The coordinates are about (22, 79). Follow the path upward.
Follow more white lines
Up and over
Ok here's where I take over. Once you reach this cliff, turn around.
Follow the cliff line all the way until you get to the next image. Note Southern Un 'Goro is to your right. You can explore that on a later trip if you want.
Climb up this hill here.
Turn to the right and keep climbing.
Once you reach the top, fall off...
and you'll land here. Keep going.
At this point fall down this cliff and keep going.
Now head up this hill, drop off, and continue.
You'll go in a straight line for a while now.
Now here you need to inch across carefully
Until you reach this point. Get a running start and make a leap of faith and go around the bend (Sorry I had my UI up at this moment)
Head down and hang a left
Make your way through these hills
Now at this point make sure you JUMP (Space bar default) or you risk falling through the world.
Head up this bend and make a turn to the left
And you've made it to southern silithus. Enjoy your fun here.
Sorry for the huge image sizes if you're not on a widescreen monitor.