I'm not 100% sure, but I believe a USB-C cable connected to a USB-C charger is cold by default until something is connected. Don't try this at home either, but it should also be perfectly safe to plug a USB-C cable into two different wall chargers.
For Alternate Mode to work, only cables with high-speed lanes will work (aka USB 3.0 cables). Power Delivery doesn't need these high-speed lanes at all.
It should be impossible for any set of non-damaged, non-defective, spec-compliant set of USB-C cables and peripherals to cause fires. The specifications are very carefully designed to prevent any combination of cables and devices from causing damage.