By definition, deserts are dry. That means corrosion is not going to be a factor. Your knife need not be able to cut back brush, but you may need it as a hunting tool or weapon. A small paring knife should be able to skin and prepare snakes (if you're into that), as well as getting into the moist parts of cactus and bugs. If you're going to have to remove or kill snakes, a large, light knife might be just the thing. I recently got a Cold Steel War Head, and I was very much impressed by its size, light weight and balance. It would be fine to use to probe holes, kill snakes and slice open cactus and so forth. You can even strap the blade onto a pole as an extension.
As for shelter, I can't help you much there. Back in the 70s, I had to live in the California desert for a few months and during that time I traveled into some blisteringly hot areas where there wasn't so much as a gas station. I was amazed that so many people had grown accustomed to it. I'm fond of cool weather with mists that roll in over the mountains and I hate seeing the sun directly. Had there been a fire hydrant, I would have tried to cram myself into the shadow. I was miserable.
Anyway, good luck. Maybe there are some desert rats here that could give you better advice. As for me, I use a solar umbrella when I have to be out in the sun.