The crosshairs should never wiggle around within the scope itself. What you are probably seeing is how much your gun actually moves by you pulling the trigger; that is why dry firing is such an effective tool, because you can perfect your technique until you've eliminated as much of that movement as possible.
The firing pin dropping actually causes a little bit of gun wiggle too, so depending on how heavy your gun is and how strong your firing pin spring is you will notice it more. I never really notice movement when I dry fire with my 12 pound 22-250, but I see them move a lot more when using my 7 pound 300 WSM
if I'm not using good technique.