I want to replace the shower head and don't want to replace the pipe. But the pipe has a
1" plus ball remaining after I remove the old shower head. The new shower head has a much smaller ball. Is the ball threaded on and can I remove the ball without replacing the pipe?

Show us a picture.

Is the ball threaded on and can I remove the ball without replacing the pipe? that pipe is called "the shower arm" and yes, it's threaded. Unscrew the old ball part and discard it. Then wrap a few turns of Teflon Tape around the threads and screw on the new shower head. Tip: The new head has a water saver installed. It's a rubber washer with holes around the edge.
If you wish more volume out of the shower pry it out and toss it. Good luck, Tom