Cut a small slice of cucumber off the bottom so the cucumber is leveled and lays flat. Make a horizontal cut in the front, about 3 inches deep, and cut out a thin slice of cucumber for the mouth.
Cut a zigzag pattern into the top and bottom of the mouth using a small, sharp knife to create teeth. Bend a toothpick in half and stick inside the mouth, so it stays open a little bit. Cut out 2 half-circles of Cheddar cheese to make the eyes and push in a peppercorn as the pupil. Let carrot slice peek out of the mouth for the tongue.
Skewer 1 Cheddar cube and 1 grape on toothpicks and stick them into the cucumber crocodile.