what is the only breed of cat without retractable claws

The only cat breed without retractable claws is not a domestic cat breed, but rather the cheetah, which is a wild cat. While most wild cats, including lions, tigers, and jaguars, have retractable claws, cheetahs have dog-like, non-retractable claws. Domestic cat breeds, including Siamese cats, all have retractable claws.