I have a large bench drill on a floor pillar, (see image 1) but one day when i wanted to drill a very fine hole( 3mm) with the same accuracy that you can with this kind of drill, i found that the chuck jaws wouldn't grasp any a drill smaller than about 8mm
so instead of whipping out and buying ( perhaps you can - since it comes with a tool for removing the current chuck) a chuck that would take finer drills, i found another way to do it by salvaging a smaller chuck from a dead portable electric drill
What you will need;
and old power electric drill
( i am sure you could apply the same principle to an old hand drill to)
screw driver to fit the screws on the drill
Step 1: Getting the parts...
2.) Locate the two retaining screws for the chuck drive bearing assembly and remove.(image 2)
3.) Then lift the entire assembly out of the drill, you may need to pry the gear wheels a bit. ( image 3)
4.) Now place the entire bearing assembly in to a vice with the chuck hanging down and use a punch and hammer to drive the chuck shaft out of the bearing - make sure you catch it. ( image 4 - hit here)
Step 2: Result
Some times you need to cut a bit off the thinner part of the shaft (away from the chuck - stage b) so that the Jaws of the bench drill clamp around the thicker part of the shaft closest to the chuck (stage a)
So first try it in your bench drill.
If you do need to remove some and don't have a cutting tool capable of doing this hardened shaft, ( like me ) then just grind down the stage (b) shaft only. DON't grind or alter the stage (a) shaft closest to the chuck or you will alter the balance fo the chuck and it will not spin true in the bench drill jaws..
and hey presto you have partially recycled that old power drill and solved the problem....