Simply put, breathing is not realistic.
Wearing a magnetic sensor mocap suit and filming you are 100% unable to see even when the actor is winded (On actual cameras you have a better chance of detecting this).
If you want to try to get some non realistic results, then you need to probably add and weight paint a couple bones, maybe even 4.
Take both skeletons out into a DCC, merge the skeletons and the meshes with proper parenting.
Add your extra bones.
Study up on how to weight paint them.
And make a basic animation to export back into the engine.