Unless you are drilling through butter – it will take an age to drill a hole using such a method. If you don’t believe me, try drilling a hole (in metal) turning a drill chuck by hand, applying the force you will be able to apply, via a socket (at right angle).
The following from ebay might suit (you would need to check the precise dimensions with the sellers) – interestingly, within the photo of the second item is shown a drill bit with a hex-drive, but it looks too long for your application.
http://www.ebay.co.uk...M&hash=item4cf5281d66
http://www.ebay.co.uk...3&hash=item5895b2b0ce