You've been misinformed if you think there's ever a chance of being kidnapped or beheaded. I lived there for about 8 months and my work might send me back because others in the company are just as misinformed. It is remote, but lots of flights go directly to all major Texas cities. The airport is an easy in and out. The drive back home for me (Austin) isn't that bad, it's an easy 8 hours. I had worse drives going back home when I lived 4 hours away in Galveston. The one hour drive I have now from New Braunfels sucks too.
As for El Paso itself, it's great. People are nice, food is great, plenty to do. As said already, really safe place to live. It has its bad parts, like all cities. When I lived there, I had to find a place quick, sight unseen, apparently a bad part of town, but I didn't find it so. Nice neighbors, park down the street, but the locals I worked with kept telling me I lived in what is called the devil's triangle. Neighbor across the street did have a truck stolen from him, but he had 4 other vehicles and left the truck unlocked with keys in it. Lol.
I miss the cost of living there, pay me what they do, feels like I won some kind of lottery. Downside for me, maybe not for you, no HEB. But I offset that with Vista Market. If your uncomfortable being around a lot of Mexicans, no matter how safe it is, then stay put. I love the place, hopefully for me I go back after the holidays, but with work, they'll probably call me and ask me to go tomorrow.
One last thing, weather is mild except for the occasional dust storm. A lot of houses have swamp coolers, so if you go looking, keep an eye out for that. Look for central air.