No need to drain the ATF fluid.
Consider replacing the seal on the transmission as per the FSM says. There is a small spring in there that is often (always?) dislodged when replacing the axle. This will result in a slow leak, really nothing more than a dampness in my experience. But in my old age I like to do things right.
I used a small claw hammer to get the seal out and the old seal to drive the new one in.
In colorado I went after the ball joint without any issues. If you don't have much corrosion in TX (which I imagine is true in the 'woodlands' but maybe not on the coast) I highly suggest it, as it's pretty easy. Also remove the swaybar endlink to give you room to get the strut out of the way. The other option is the 2 strut mount bolts. One is the camber adjust, so make sure to mark it clearly and take a picture.
Also, don't loosen the axle nut on the ground, it can lead to bearing failure. Do it on the air. Some have someone stand on the brakes, I used a board and my power seat to depress the brakes.
Pull the axle out of the transmission is easy.
Make sure to use an OEM axle, otherwise you risk a vibration issue. I got a used one to replace an aftermarket one that was causing a vibration under light acceleration. I was surprise that was the fix, but I'd tried all the other easy things.