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Originally Posted by MID1
If it was hit "up", it would establish itself in a higher orbit, and slow down as a result, and this would also happen if it was hit "back", behind the station's path of flight. The cosmonaut would actually be reducing the ball's velocity, which means it would probably stabilize itself in a higher orbit (no way he could-de-orbit the ball, I should think, and with a 6-irn, if he hit it square, he'd be hitting it up as well as back).
If it is hit along the flight path, the increase in velocity would make the ball drop into a lower orbit.
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I believe you have this backwards. Hitting the golf ball along the flight path increases its energy, thus putting it into a higher orbit (where, ironically, it will be moving more slowly), and vice versa for hitting it opposite the flight path.
I would vote for hitting it in the opposite of the direction the station is moving. That would put it in a lower orbit to start with, and as a smaller object its orbit will decay faster. So that way it should never be an issue for the space station.