How do I safely discharge this capacitor with broken wire?
I would take a 0.25W 10k ohm resistor, hold the ceramic body gently with a pair of pliers, bend the legs so that they will fit between one connector contact and the nick in the wire and hold it between the two. Keep in in place for a second or two, and once done use a voltmeter to check the voltage across the same two points. When it is properly discharged it should read less than 1 volt. If it reads more, repeat the above.

If you use a piece of wire / screwdriver / other short circuit you will pull a huge current (for a short amount of time) from the capacitor - you will see this as a momentary arc (spark). This could damage it - it is certainly not designed for arc discharge given the application you have pulled it from.