Shakespearean England (as with the rest of Europe) looked to ancient Greece and Rome for its cultural touchstones, and much of its knowledge about the world was derived from classical authors. Crocodiles were known in ancient Rome, one piece of evidence is Roman historian Cassius Dio who describes them being used for entertainment at the circus. The original Dio is here. There are other accounts of crocodiles like the writings of Strabo (see the first link).

The Greeks and Romans knew of crocodiles because Egypt had been part of both Greek and Roman empires, and Nile crocodiles are native to Egypt. Crocodiles were also present in ancient Egyptian culture (e.g. the crocodile god Sobek.)

The education of someone like Shakespeare in 16th century England would have been dominated by the classics, including the sorts of works mentioned above where crocodiles are described. Perhaps not everyone in his audience would have heard of a crocodile, but clearly he thought enough would have that it was worth including the line.