there is another variation of an old tip that also works
Take an old electric knife, and instead of dulling the blades and taping a pill bottle on one of them, make one into a mounting point for a removable pin.
mount the knife onto a board, anchored nice and solid. put another shorter board on channels on the long board. mount a pair of angle brackets onto that top board, pinning the dulled knife blade in between them
mount two of those cheap plastic flip lid compartmented boxes onto the top board. You would then load up your paint bottles in the boxes, close the lids and turn on the electric knife
A simple rheostat in the power line would cut the speed down to just a back and forth "shush, shush" as the beads move back and forth inside the bottles
If you have ever made the one that people link to online, you know that the force and speed is too high with the knife running at stock speed
just like if you get the wheel spinning too fast,,,,,,,the beads don't move up and down inside the bottles, they stay in one end (that means that you know that there is no stirring going on, beads or not)
shaking by hand is perfectly fine, too,,,,,,,,,,but, those of us with Arthritis may have aggravated that with all the paint shaking through the decades,,,,,and even it it didn't contribute, it is no picnic after Arthur comes to live with you. I also have over 700 bottles of paint now,,,,shaking with some sort of tool is sort of mandatory these days (even if I only mix what is going to be used on "today's project",,,,,that is in the area of 20-30 colors on each aircraft)
Rex