You haven't provided enough information for a meaningful response.
How can the capacitor you built be "charged with a 20kV AC square wave from a modified domestic ion generator?" Capacitors are "charged" with DC not AC. What model and manufacturer was the domestic ion generator before you "modified" it? What modifications were made? Be specific in your answers and provide a schematic clearly illustrating your modifications.
There are good reasons why high-voltage oscilloscope probes are expensive, and why their high-frequency response is limited. These probes must be carefully matched to the oscilloscope you are using and proper high-frequency compensation adjustments made, a procedure you are probably not qualified to perform. More information can be found at the
links provided by this Google search result. You can find similar results using other search engines. Try searching with this string as the target: "high-voltage compensated oscilloscope probe theory."
There are non-contact methods for measuring voltage, but while simple in principle they are complicated in practice. An electric-field mill can be used to modulate the field surrounding the capacitor, thereby allowing a small voltage, proportional to the voltage "seen" by the field mill, to be produced. Modulation is typically performed with a motor-driven "chopper" and the high-frequency response is limited by the modulation frequency to a few hertz. I used one of these devices to measure and control the acceleration potential, up to 1.7 MV, of a tandem particle accelerator.
If all you need "is a visual, or relative, approximation of what is happening, not actual measurements" then a leaf electroscope might be an inexpensive approach. You can build one of these yourself using just an insulating cork, a copper wire, a glass jar fitted with the cork, and thin strips of aluminum foil. Insert the wire through the cork and provide an "L" shaped bend inside the jar to support a strip of foil. Use a drop of superglue to secure the center of the length of foil strip to the wire. Bend the two foil "leafs" down so they are parallel and touching each other. Voila! You have built a leaf electroscope.
More information can be found here.
Early adopters used gold leaf, probably because it can be hammered into very thin sheets and is "heavy," but I found that some types of capacitors could be disassembled to salvage very thin pieces of aluminum foil used for the capacitor plates. That may no longer be true today, because it is easy to metalize thin plastic film to make capacitors. Worth investigating though. You can also purchase gold leaf and other thin foils from art supply stores.