There isn't actually a requirement to use a X cap in a capacitive dropper, in fact some capacitor manufacturers discourage it due to the thinner metallization and progressive capacitance loss (it needs to be rated rather higher than 400V though). You can have UL (flammability) without X rating. The onus is on the manufacturer (you in this case) to ensure that the entire circuit is safe, not just individual components.
Let's look at your circuit, as drawn. If they capacitor shorts (even briefly) then full mains current will flow. The 6V2 Zener will take the brunt of it and probably fry first, then the either the bridge or the NTC thermistor will blow (assuming the zener fails short). Clearly protection is needed.
You also have the issue of mains spikes (even turn-on spikes at mains peak). The capacitor impedance will pass a nice predictable current on a 50/60Hz sine-wave. When you hit it with a fast edge, it will pass a great deal more current. If there's sufficient energy, it will start taking out parts, and a fuse won't be quick enough. You need a series resistor to limit these spikes. If you put, for example, a 330R resistor in series with the input, this will limit these spikes to less than 1A. With properly rated parts, the circuit can mop those up.
Now we come to the issue of the capacitor shorting again. The resistor will try to dissipate all the power between mains voltage and the 6V2 clamp. To overcome this you should make this resistor a flameproof fusible one. It will go open circuit cleanly and without fuss in these circumstances.
Yes, it would be advisable to fit a fused inlet too - the PCB might break or something come loose if dropped for instance, but you wouldn't normally expect it to act fast enough to open with a component fault, the fusible resistor will go first. You should pretty much always use a fuse at a mains input, it's the last line of defence.
P.S. Do you really mean an NTC thermistor there?