If you use the interstate going west from Kent to Van Horn, TX on the ST, the first exit into Van Horn is narrow and does not have the usual side lane. It can be heavy with truck traffic that would run you over before slowing for you. Other than that one exit, most have plenty of room. You do not have to cut across to use any exit. You will see a sign for an exit. Keep to the right.
If you are cycling on past the exit, what you do depends on traffic conditions. It there is no traffic coming from behind for a very long way, don't worry about it. Just keep going. If there is or has been quite a bit of traffic, here is what you do. Stay to the right. Cycle to the point on the exit lane where the road is at its narrowest or nearly so. That way you can cut across and get to the other side in the shortest possible time. When you see a space in the traffic, make your left from that point.
When you simply continue on at an exit, it can take a considerable time to get out of the area where you can expect traffic coming on from the rear. If you go straight, make sure you have the time. Vehicles moving at 80 mph may seem like a long way off when you check your mirror, but they can be on top of you sooner than you think. Taking a 90 degree left turn at the narrow point of the exit lane will get you into the non-driving zone in a heartbeat. Always check carefully before you make the turn. I have been in traffic so dense I had to wait and wait just to get across a 25 foot wide exit road.
By and large, you will be safe from being hit by a car or truck as long as you are cautious. Be safety minded at ALL times.