You may not be able to see a crack with the naked eye. It may even be difficult to see it with a magnifying glass.
The lock washer may work.
Not sure about a longer screw, you may not be able to tighten it up properly.
Adding a toothpick will probably just crack the handle's screw receptacle.
Why not just replace the handle.
Click on the picture for more info
Part number: AP3906094