Any way to add shadows to a scene without adding additional lights?

A bit of an odd request, but we want stylized shadows that don't necessarily reflect the lighting of the scene. Basically, we want the scene to be realistically lit with baked lighting, but we also want clearly defined shadows of the characters on the walls.

My first thought was to add a light source pointing directly at the character, but I can't find a way to not have it contribute to their lighting (which would make them look washed out). I also saw people talking about projectors, but I'm worried setting them up may be tricky for a live character, and they may not be performant (we're targeting mobile).

So I'm wondering, is this something that's possible to do? FWIW We're on Unity 2021 with the Built In Render Pipeline.