Choke filters are not recommended. They can cause additional voltage spikes. And insulation is also a problem if the chokes are too tight wound and too small - high voltage will jump over the choke then. There IS current flow at deeper than skin depth, even at four or five times skin depth, but it decreases fast. Not webers, or inches, or anything more complicated.
Copper has relative permeab.
Skin depth is thus 0.233 millimeters. The streamers from the secondary are dangerous to even lethal , because the RF frequency lies outside the nerve cells detection ability which means that you don't notice that there are 100W of power travelling along your tissue and blood vessels, cooking you from inside out. Instead, use long plastic rods with an end metal terminal that is connected to ground. With this, you can safely draw arcs off the coil. In this way you get maximum power transfer from the primary tank cap to the secondary self capacitance.