If you've got the needle, I've got the sharpener:
http://ftldesign.com/images/NeedleSharpenerKacti.jpg
Clamp the needle in the chuck, twirl the red handle, and the needle is automatically rotated while simultaneously being spun around the annular sandpaper surface.
The base of the sharpener is also the lid of the storage case, and triples as a record duster. U.S. Patent 2,099,179, 1937.
And from the other side of the ocean, this model by BCN (price 3/6), working on a similar principle: