Whether it is a shotgun slug or an Accelerator bullet (.223 caliber bullet in a .308 caliber sabot), their sabots/wads can damage the chronographs. Sabots and wads are designed to separate from the projectile right after leaving the muzzle. After the separation, their trajectory may slightly change in an unpredictable pattern. Although the sabots and wads are lighter and have much lower velocities than the actual projectiles, they can still pack some punch, enough to damage the chronographs or any other fragile equipment (cameras, Decibel meters, and whatnot) on their way.
If you shoot shotguns, you have probably seen the wads hitting the target at close ranges. Sometimes they can even pierce a cardboard target or get stuck in it. Apparently, this is also the case with Accelerator sabots. In the video below, Accelerator sabot breaks the display of a chronograph.
Possibly, a solution to this issue could be some sort of a shield placed in front of the chronograph display. It will need to be made of strong enough material and firmly fixed in place to stop/deflect the sabots. It would also be good to have that shield made of a transparent material to make data reading easier. However, be careful when experimenting. The described setup will probably have a danger of ricocheting sabots and wads.