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Maybe try a magnetized round shaft screwdriver.
Or a length of small tubing on the ball, the other end of the tubing attached to a syringe, then pull the syringe to apply a vacuum to hold the ball. Or put the tubing in your mouth & suck to pull & hold a vacuum to hold the ball to the other end of the tubing. If you don't have tubing, try a straw.
If you don't want to put the tubing in your mouth, apply a little sticky fast drying adhesive to the end of the extracting device & take a coffee break while the glue sets on the ball.
Some thoughts for pondering of things I've had luck with, extracting hard to access items, let us know what works for you.