As long as your chrono hand has a good rivet, you should be able to tighten it with your staking tool.
After centering the staking table with the centering stake, place the hand -- tube up -- into a stump that allows the face of the rivet to sit inside it.
You want the face of the hand wand sitting flat against the stump.
Install a convex stake that allows the tube to fit into the hole at the end of the stake with as little play as possible, but so that it slides in easily.
You want the round face of the stake to fit around the tube & sit against the back side of the rivet.
1 or 2 LIGHT taps with a brass hammer should tighten the rivet joint. DO NOT BANG ON THE STAKE OR YOU WILL DAMAGE/DEFORM/DESTROY THE HAND!
Remove & check for tightness. If still loose, repeat.
Once you try it, you will be surprised at how simple the process is (& why you did not do it sooner).
Good luck.