Credit goes to Spudley for giving me the ideal for this.
Materials needed: J-B Weld, large diameter straw from Mickey D’s, tool of choice (Phillips, Allen, Torx, etc.) and masking tape.
Top: The bit has been reduced in diameter to fit inside Corkscrew. Notice the shank of the tool has been further reduced to approximately the same diameter of the original mini-screwdriver. This is to provide an extra margin of room for the epoxy to grip once the deep grooves are cut for insertion into the Corkscrew.
Bottom: The bit has been wrapped with enough masking tape to plug the inside of the straw.
Look at the picture of the bare bit, notice all the grooves? I purposely used a coarse double-cut file to get them. I feel this should give the head plenty of grip so flats should not be necessary. Be sure to de-grease the bit before applying the J-B Weld.
This is how the head will be molded; fill the straw with J-B Weld. To avoid trapping air bubbles, drip small amounts onto the end of the shaft and let it run down on its own. The J-B weld has a decent working time, but you may want to do it in two batches.
Top: The J-B weld has set up and removed from the mold.
Bottom: The corkscrew groove was cut using a round Swiss file, starting at the bit end and frequently checking the fit on a corkscrew. If you botch it up, you can just fill it with more J-B and start over.
This is really only suited for low torque applications like the screws in personal electronics.
Edited from the forum discussion by Defender