Do you even need to handle the shadows in the calculations?
You could as I said simply cast a ray from the light source to the bullet when it hits something and see if the ray hits the player right before the bullet.
Of course this only works with one light source realistically but it should be fairly accurate (accurate enough for a game).
Otherwise you would have to check for every shadow from every light source which include shadows that do not show up because they are illuminated by a different light source.
Given his experience level and the concept being a bit shallow, he should concentrate on getting the core idea of the game (shooting shadows to hit entities) in a more easy or at least solid way done.
I still think the idea is awesome and could be a really great game.
Maybe start writing a design document and put down a few more infos for others to contribute before going for the best solution.
It could be that the best solution for hitting a shadow is not the best solution for your game.
On a side note: Shooting the shadow can be fun for multiple players but keep in mind that AI does not necessarily see the shadows and won't shoot them. Coding an AI that is aware of all shadows might be the harder part than the shooting of the shadow itself.