Personal confession time:
I'm NEVER not afraid when I go solo. For me, that's part of the hiking experience....there is a heightened awareness that comes with healthy fear. A rush, if you will. As the hike progresses that fear settles down to more rational thought as I get use to my surroundings. That fear is a large part of the personal challenge of backpacking and very likely why you are doing what you are doing, Tarbubble! It certainly keeps me coming back. After a day and a night on the trail, your fear will melt away into healthy respect and you'll probably find yourself disappointed you didn't see a cat! Sightings are rare which is why rangers want to know about 'em. Attacks, even more so. 1 attack makes world news and those attacks are usually circumstantial.

My favorite backpacking/camping place on Earth (my ashes will be scattered there <img src="/forums/images/graemlins/grin.gif" alt="" />) is Big Bend National Park. There are over 2 dozen known lions in the park and more coming....to the point they don't track them with radio collars any more. I go there twice a year and have been doing so since 1974.
There are cat "attacks" reported there almost every year. I've car camped all night long peering through telescopes, solo hiked and camped for days, hiked the river, mountains, etc. My park cat sighting count is...........zero....in over thirty years.
In fact, my last solo trip there I specifically asked the ranger for a back country campsite where the last cat sightings were, hoping to see one. No luck.....but, I'm still very cautious.

One stress reliever I find works is to loudly call out "Here kitty kitty kitty...." when the trail gets curvy and you find yourself frightened. You'll likely start feeling goofy and start laughing. <img src="/forums/images/graemlins/cool.gif" alt="" /> Especially if another hiker hears you and says "meeeooooowwwww" back. (happened! felt like a dork)
Most 'attacks' in the park were because of kids startling a sleeping animal or surprise encounters. Stalkings have been reported by trail workers using burros to haul equipment. Animals were easily chased away. Rare sighting all the same. If they weren't rare, we wouldn't hear about them, inverse of what you might think.

I consider cats and bears the same as sharks and alligators. Not dangerous unless provoked and a treat to see in the wild. Sure, be afraid, but try and be rational and look at the 'big picture'. Those critters are rare. Dangerous people are a lot less rare and bad drivers even more so.

By day two, you'll wonder if you'll ever get to see a beautiful cat! <img src="/forums/images/graemlins/grin.gif" alt="" />