Push hands doesn’t use energy transference, but energy flow. It’s purpose is to teach the practitioner to move with the energy of their opponent, not against it. You don’t actually take the energy into yourself.
It would no more give you your dad’s cancer, than if he breathed on you.
As @Maulbeere mentioned above, 8 Brocades qi gong can help with healing. There are many varieties of the exercises available. I learned a version of them called the Precious Eight, from an old book called The Power of Chi, and the author describes using the exercises to heal his lung cancer. They act as both a way of healing and a way pf prevention.