The only thing that pops to mind besides using a hammer ... and tapping gently .. is to roll the needle 'taper' part between two hardened flat surfaces, such as two pieces of sheet steel. The needle would be forced to go to minimum distortion if it were rolled back and forth. Not to say it would not try to 'walk' out of its 'bind', but I think it would do the best job if time were taken. I am imagining the needle to be tapered from the threads down to the tip, and if it is a different style, YMMV.
tom
tom