STK includes a powerful calculation for computing conjunctions with Space objects from known (or unknown) missile trajectories.
A known trajectory can be applied as well as a time span around that trajectory and along with uncertainties in the launch and impact locations. All of these are then rapidly computed against a satellite database to identify clear-firing or blackout windows.
This tool can be easily accessed by inserting a Missile object into your scenario, defining its trajectory, and then right-clicking it in the object browser and selecting Missile -> Launch Window Analysis.
Please reference the STK Help on
Using the Launch Window Analysis Tool for more information.