How feasible are electrostatic pellet guns?

I will make the assumption you are interested in the “charged” portion of the “electrostatically charged metal pellets” in your question. We already know how to fire metal pellets electrically and can do it precisely to astonishingly high speeds.

From your question I think you are trying to disrupt an electrical device activity at a distance.

I do not know of a technology that permits captured electrons to carry any significant energy for a sustained period over a distance. Pith balls have a high stored charge to mass ratio but they do not hold it for long and their low mass does not permit delivery over distances.
Mechanical energy in the form of kinetic energy imparted to a mass is quite effective at distances. Since you are trying to disrupt an electrical device I would suggest a projectile with an electrically conductive payload: carbon fiber nanotubes bundled in a regular pattern and packaged into a sabot with a timed disrupter A millisecond or two before impact the sabot opens and the carbon fibers tubes are delivered at high speed into the circuitry. The conductive tubes embed themselves and producing both open and short circuits in random locations resulting in device behavior that can include: no-op, unpredictable and uncontrollable, and total destruction.
Wear your safety glasses.

@LuckyGuy
I was actually more thinking about taser-like anti personnel usage.

OK . Let me make sure I understand. You are not looking to use the ESD to disrupt electrical signals. You want it as a non-lethal anti-personnel device. Correct?

If yes, then how about letting an electrically powered, mechanical device do the physical disruption. There are battery operated electro-mechanical delivery systems that provide impacts of ~1.5 Joule at 600 rounds per minute. While not lethal you would not want to be on the receiving end of such a stimulus.

”how about letting an electrically powered, mechanical device do the physical disruption.”
Because I want to shock them with juice. Kinetic weapons are just so boring.

Would a 1.5 J burst of mechanical energy (imagine being hit by a paintball pellet) feel different from a shock? Either way it’s going to hurt
It sounds like you are looking for a hypothetical pellet that is filled with free electrons rather than paint. That old rule: “Opposites attract. Likes repel.” is going to be hard to beat.

How about sphere shaped capacitors? I heard they can hold a charge for quite some time?

There are ultracapacitors that hold a lot of charge 1 F. but at a low voltage. 2–3 volts. I have never heard of a sphere shaped. They are always in cylinder form so they can be wound. Something on the order of 10 mm diameter and 20 mm long might hold 0.1 F max. You might have to invent a stack of them to get the voltage up.

Check out Maxwell BCAP0003 P270 T01, 2.7V, 3F, wire leads 10mm diam, 20 mm length, Mass 1.7g

Stored energy: 0.003 Whr, 10.8 Joules

It’s got the right energy storage. You want to trade off capacitance for higher voltage. Good luck in your search. you might have to invent it.