In the script that takes care of the cursor or mouse navigation, you can make a conditional, like this:

var allowNavigation : bool = true;

if (allowNavigation == true) {
    ... your cursor or mouse navigation code here ...
}

You can then switch that variable, allowNavigation, off and on based on timing in the animation. A few ways to do that:

• In Update(), check if the time of the animation state is within certain values, like this:

  var animTime = animation["myClip"].time;
  if (animTime > turnOffTime && animTime < turnOnTime) {
      allowNavigation = false;
  else {
      allowNavigation = true;
  }
  

• Use the Animation View to add AnimationEvents in the animation clip which call a function that can turn allowNavigation on and off.*

• Use the Animation View to animate the allowNavigation variable directly. A value of 0 mean false and 1 means true. You can use stepped interpolation.*

*** These solutions doesn't work on imported animation clips, since they are read-only. However, they work on animations created directly with the Animation View, or on duplicates of imported animations.