NeoTech,
Even though I have described a relatively complicated stepped inside mandrel/collet I think you were on the right track from start.
After having thought a bit more, my design would be something like below:
A short housing with a wider "collar" at its lengthwise center to be stop for the chuck jaw or collet nose. The back end would be drilled out so I could fit a long nut. The business end would be turned to a close fit in the part it shall hold and then drilled/bored out so it is just about 1.5 mm thick. Then cross cut to be expansionable.
A cone with suitable diameter to fit inside and a bit of threading to pull the cone in using the long nut. The cone shall preferably not protrude outside the thin end so the collet can bottom in what it shall hold.
Now pull the cone into the collet and there you have it.
I would rather use a nut to pull the cone in insterad of a screw as there would be a risk that the screw will push out the job if too long.
When it comes to measures I would go for the same length of the business end as its diameter (if not very large), the support collar about 3 to 5 mm in all sizes and the back end around 20 mm to be good enough for chauck jaws and collets.
Just another idea...
BR
/Peter