The real story
The lesser mouse-deer, Tragulus kanchil, is the smallest known hoofed mammal: about 45 cm long and around 2 kg. It isn't actually a deer but a chevrotain, an ancient branch of the hoofed animals; the males grow no antlers, just small tusk-like canine teeth. In Malay and Indonesian, 'kancil' is also used for a clever, cunning person.
The crocodile story is told across Indonesia, Malaysia and Singapore. In many versions the mouse-deer claims to be on a mission from King Solomon to count every crocodile in the river, and clever-mouse-deer stories also appear in old Malay texts such as the Hikayat Pelanduk Jenaka. The kancil who steals cucumbers and gets caught by a farmer belongs to a different, equally famous tale.