El Paso is no more dangerous than Albuquerque, Phoenix, or Tucson. In any city, you're going to risk having things stolen out of the back of your truck if it's not covered and you're not watching it. That's just the nature of things. Get a tarp.
I usually avoid the I-10 route because of that stretch between El Paso and Boerne. Not because of any trumped up, sensationalized news stories about the border, but because it's horrendously boring. I've found US 90 to be more interesting, but it's out of the way from Austin. TX 71 to US 190 is also a little more interesting. But they'll add time to your drive. Jumping up to Flagstaff will add a lot of time.
If you're worried about getting the drive out of the way, then I would suggest you not visit the Grand Canyon this time. Just visit it again another time, when you have more time. I helped move my friend from San Antonio to Rancho Cucamonga several years ago, and another from Houston to Los Angeles a few years before that. Doing it in two days is really pushing it, to say the least, particularly if it's just you in the car. If you have "extra" time, I would suggest cutting your daily drive times and taking three days to do it.