As I see it, the important uses of a motorized stirrer are to:
My first test had a radius of about 4.5 inches, which made it very fast, but had to be held in the middle of the bucket, and couldn't reach the edges.
So I tried: a diamond shape, and a triangle with the end being a relatively flat part, and then the shapes shown, which are simply rounded and open. By the way, if you want to make them, at first I tried heating the steel before bending with a propane torch, but later found it was just as easy to do it cold with a vice and pair of vice grips.
Anyway, most shapes work, ( a circle or jelly bean shape would be good, if you could do it) but the one shown on top in the photo, which is about 3 inches across, seems the quickest for stirring. (I scrimped a bit on the lower one, so I could make two from one 3' piece of rod). I think having a flat part at the bottom helps for getting corners and encouraging glaze through a sieve.
If you want to try to make one, start
with a piece of 1/4" rod about 20" long. Using a vice and some vice grips,
make the first bend 5" from the end, about 45 degrees angle. This is, in the illustration, the first bend shown after the long straight part.
Make the second bend about 1.5 ", aiming it back towards the center of the rod. Finish by bending up the last inch or so, possibly even back in towards the middle so it doesn't scratch the side of the bucket. When you're done shaping it, balance it by setting it on a level surface with the shaped end protruding. Whichever part hangs down, bend the whole hook the opposite way until it doesn't roll when set down. Good luck.
Always use it when spinning submerged, or it will spatter glaze all over. Keep hair, clothing, and body parts out of it, and you'll do well.
Addendum: In the end, I've reverted to a chain style mixer, because I think it does a better job. But this one works well and is easier to make if you can't weld....