I've only driven parts of I-40/Route 66 so I may be wrong on this but you are mostly driving through flat-land states like Missouri, etc. No mountain drives are on this road that I'm aware of. I'm sure someone will correct me if I'm wrong.

As for mountains, I think your fears may be ungrounded on these. While there are certainly some windy, twisty roads in mountainous areas, most interstates are fairly straight, wide, and have ample shoulders/rails/etc. to keep you from any drop-offs they may have. But, in fact, most interstates going through mountainous areas don't even have any drop-offs to speak of.

Just a thought, you may want to explore some of these roads once you get settled in your new home. Colorado is close by and has some fantastic scenery and historical areas that you would miss by avoiding such roads. In fact, mountainous twisty-bits are my most favorite types of roads to drive. Fun to drive, great scenery, etc. I think you should give them a try.

However, they shouldn't be a factor during your move to Las Vegas if you stick to I-40.