I frequently use an old cordless drill chuck to hold bits for cleaning up holes in my prints. Finally decided to make it somewhat less awkward by mounting that on a handle.
Most small US drill chucks mount on a 3/8" - 24 TPI (fine) thread. I wasn't able to find AllThread in this size at the local home improvement stores so I ordered it from Amazon.
Get some AllThread or cut off a bolt head and epoxy it into this handle. Then screw on your chuck from your old, run down cordless drill for a quick and easy way to hold your drill bits without tearing up your fingers.