Capacitor Selection for high voltage
Yes, you can have kilovolts on very small value capacitors.

This is a Wimshurst machine.



It generates around 30kV.  

It has no explicit capacitors for storing charge.

It has only the inherent capacitance between the two iron bars with the large balls on the ends. 

That capacitance is some few picofarads.  It is still enough.  It charges up, and discharges at around 30kV.  The spark will jump a gap of 10 millimeters.  Since the capacitance is so low, a full power zap from it doesn't hurt.  I routinely discharge it by touching the bars.  If it had a capacitor of any size on it, I wouldn't touch it.  That would be painful to deadly.

As others have said, the value of the capacitor says nothing about its voltage rating.  

The voltage rating depends on the dielectric, how much dielectric is between the electrodes, and the separation between the electrodes.

This is a 1 nanofarad SMD capacitor size 0402 rated for 50V:



Not even 1mm on a side in any direction.  Costs about $0.50

This is a 1 nanofarad ceramic capacitor rated for 30kV:



It is 30 millimeters in diameter, and 19 millimeters thick.  Costs about $30.

Clearly, the capacitance says nothing about the voltage rating.

The voltage does however make an enormous difference in the stored energy.

A fully charged 1 nf, 50V capacitor can store 0.00000125 joules of energy.

A fully charged 1 nf, 30kV capacitor has 0.45 joules of energy stored.

The voltage matters, but not the way you thought.