Does having short toes decrease your chance for hammer toe?

No: Hammer toes can be caused by ill fitting shoes, biomechanics, alterations of tendon mechanics and many other processes.

While any size : Toe can hammer, i find clinically the answer to be yes.

Short or long: The toes can be short or long. A hammertoe is an contracture or a bending of the toe joint which results from a muscle or tendon imbalance due to the mechanical and structural changes that may occur over time. This can be hereditary or due to environmental factors such as tight shoes. This bending leads to an abnormal pressure distribution resulting in pain, swelling, blistering, and corns.

Not generally. : A hammertoe is any toe that has contracted, either from a tendon pull or from arthritis. The length of your toe generally doesn't matter, especially if you wear appropriately fitting shoes.