I've wondered about making my own stun darts too and found several variations that work well and a few things that didn't work well.
For the cones of my stun darts I've used soft drink bottle labels, thin packing tape stuck on to 1 layer of newspaper, duct tape, extruded milk jug plastic (HDPE), these HDPE cones tended to be thin and didn't hold up well with repeated use and packing tape on 1 layer of soft drink label.
In the picture below the stun dart to the left is the extruded HDPE, the red white and black cone next to it is made from a soft drink bottle label colored with maker pens, then a combination packing tape newspaper cone, a duct tape cone another packing tape cone and the cone laying down is made from a combination of packing tape on a soft drink label (notice the label design inside).
To give them weight and hitting power I used a sheet metal screw as the head and 3 copper coated steel BB's all held in place with hot glue. Try to keep the filling (BB's + hot glue) in the less than half the length of the cone toward the front keeping it to a 1/3 is better for good flight characteristics. I have used Plaster of Paris (PoP) as a fill too but made the mistake of nearly filling the cone and that wrecked the dart flight.
The BB's can be seen inside the 1st dart and just barely in the dart laying down. I used Gorilla glue in place of hot glue (duct tape dart) and it works but is more difficult to control. These stun darts are easy to make, hit surprisingly hard and are fairly robust. All of them for my .625 cal and weigh between 2.5 - 3.0 grams. Lead shot and bigger screws would increase that weight.