fang
One four letter animal that does not rhyme with any words is wolf.
craw
Wolf.
Click
'Hare' is a four letter word for an animal, that starts with the letter 'H'.
fawn
Pelt
colt
mole
Neck is a four letter word for the part of the body between head and chest.
Part
Goat can be formed from the letters in "dogmatic".