Almost every time a crocodile shows up in Shakespeare, it is in its metaphorical sense of one who cries false tears. The mentions in Othello and Henry IV both expand on this idea and deal with it explicitly. The references to crocodiles in Antony and Cleopatra may also hint at the tears aspect of crocodiles and then there’s this one.
It always seemed to be a line about doing something impossible and ridiculous – like a crocodile is big and tough and would be incredibly awkward to sink one’s teeth into.
But seeing as how Shakespeare mostly referenced crocodiles when accusing people of false shows of grief, I read it more as a challenge to Laertes’ grief. Maybe by consuming a crocodile, one might take on his false tears of grief as well?
That is, Hamlet offers to match Laertes’ tears of grief ? Hamlet offers to match Laertes’ tears with the consumed crocodile.
It’s not very fair to the crocodile though.