I would not make that presumption that the circuit shown in the posting is known to work properly. The resistor for the LED does suggest 12 volts supply, but since we are not given any hint as to what effect that capacitor is intended to provide I am inclined to avoid making any guess. Consider that we have no statement as to the intended output current, and the frequency is a guess based on the values of the timing components.If I make the big assumption that the circuit you show is known to work properly, and you're basically asking what capacitor should you use, then I believe you're after a type X, I'm not sure if a type Y would be appropriate here. Here is some reading on capacitors for high voltage AC like you have.
by Jake Hertz
by Duane Benson
by Aaron Carman
by Aaron Carman