Well ;
I like reading all this . I personally use the built in paint shaker on the end of my left arm . While it's lost some usefulness it is great for gripping and shaking these paint bottles . The hand completely encases the bottles ( no spin -out ) and even when done shakes slowly for some minutes , letting the paint inside calm down .
Seriously , I do have a paint stir machine built from a discarded electric tooth brush ( Battery Powered ) and a circular one built from a mini-rotary tool I bought back in the sixties at the base hobby shop in Bremerton , Washington . Never had seen a rotary tool that small , Battery Powered and it has always worked great .1/2 speed only !