Best thread title, ever.
Yes, you can refinish with either abralon or with wet-sanding strips (abralon is easier) by hand.
The trick is to keep track of the area of the ball (start over the logo, do that hemisphere, flip it over, etc. Work with a wet sanding media, light pressure, and use the same motion everywhere you sand for a consistent amount of time.
That will keep the sanding even and not get the ball out of round over time.
It's a lot of work, compared to a spinner, but nothing at all wrong with sanding yourself.
You can look up the grit steps on your ball, or modify to suit your tastes. In general, if you have a 2000 grit finish let's say, you'll want to do a 320 grit, then 1000, then 2000. Work in even steps up to your final finish.
There are exceptions to that, but it's a good practice on most finishes.