Trying to get a completely transparent mesh to hide parts of another visible mesh it overlaps.

Been trying to wrap my head around how to get this concept to work and I'm not sure where to get started. I have a 3D model character wearing a 3D model prop and I'm eventually going to use facial tracking to map them both (I.E. the user moves their head, the 3D model character matches the movement, that sorta thing.) and in order for it all to work the way I want it to, the mesh of the 3D character is entirely invisible with just the prop visible, so it looks like the user is wearing the prop. I need the completely invisible character model to block the parts of the prop model mesh that it overlaps without affecting anything else in the scene, but I'm not sure how to do that in Unity. Any ideas?