I've some idea of how to proceed, but they all have some issues. At the moment, I'm looking into https://docs.unity3d.com/Manual/SL-ShaderReplacement.html with a two camera setup.
Ideally, I would like to have the materials be renderer as is and then modify the resulting color to add the transparence. Maybe I could draw all near object into a texture (1 per object), then reuse those texture to redraw with an other shader that would sample those texture. However, doing that seem to be really intensive computationally.