I saw the video and thought conductive tape foil would work better because you are working with signals around a flat plane the build isn't much harder. Stick the foil to a surface, cutting the foil into shape, add a layer of insulation tape and then add the shielding tape to overlap the edges of the insulation layer. Then add another layer. Maybe adding some compression between a few steps could help to shave off the millimeters but it runs the risk of ripping the materials. Both copper and gold foil tapes are available and gold foil tape would improve sensitivity with out much cost.
Some cooking utensils have a nice silicone thermal resistant and electrically insulated material that people may want to chop up into strips to finish off their probes in case they touch their probe to something hot or high voltage.
https://youtu.be/2xy3Hm1_ZqI