If you're using the transistor to connect the capacitor to contacts on the birdfeeder, be aware that the current may not be as small as you hope...capacitors can develop very high currents when shorted out. I'm unsure of the typical figures for electrical resistance of squirrels...but that capacitor can be quite lethal to humans if it ends up discharging across your chest. Even just discharging into your hand could cause serious injury, either directly or through uncontrollable muscle contraction.

A better tactic might be to do the switching on the low voltage side, only turning the flash charger on when you want a charge to be present. Put a resistor across the capacitor to make it discharge when not being charged, perhaps reduce the size (but not the voltage rating!) of the capacitor to make the circuit respond faster overall. Removing the capacitor entirely might actually be best, the charging circuit might put out enough current on its own to deter squirrels.

You might do the job with a much simpler circuit. Any decently high inductance coil can give you a "bite" if a current is established through it and then removed while you're touching its contacts. This is the basis of the flash charger circuit...the growing or collapsing magnetic field of the coil induces a current in it, causing inductors to "attempt to maintain" a constant current. When a current is established and then the circuit is suddenly opened, the voltage across the inductor can become very high. If you hook an ordinary electromechanical relay up as a buzzer, with the coil in series with the normally-closed contacts, enough voltage might develop across the coil to deter squirrels, and the relay will generate an obnoxious noise to add to the effect.