Check first that the chuck is original. A replacement chuck can cause key fit issues.
If the right key never shows up, a thin sleeve will work. Brass or steel hobby tubing is usually close in size, or even a wrap of feeler gauge stock epoxied to the pin.
The cartridge case idea will work but likely won’t last long.
At that point, replacing the chuck with a quality 3 4 unit is the clean long term fix.
