Disable mesh renderer of gameObject for one camera only (without use of culling masks)?

I'm making a multiplayer game where each player has their own first-person camera. I want each player to see all of the other players, but disable their own character's geometry so it doesn't occlude the camera, which, for other design purposes, must remain inside the mesh. The go-to solution for this would be culling masks set up for each camera with each player belonging to a different layer, but layers already being used for other purposes. Can I simply disable the player geometry's mesh renderer for their specific camera? How would I go about doing that? The camera and geometry are both children of the same parent node, if that's useful.