The tail is the key to this bird. All Cooper's have graduated tails. That is the central tail feathers are longest, and the outer feathers are shorter, which can be seen well on a ventral view like these (however, you usually can't tell from behind with a closed tail). The breast marking on a juvenile Bird is different, the Cooper's have fine, narrow marks on the breast and the Sharp-shinned have broad wide marks.
Note the dark nape (back of the neck) that is darker than the crown. Diagnostic for Sharp-shinned on an adult bird like this one. A Coop would have a dark crown / pale nape combination. This is reinforced by the small head, short neck and small bill.

Supporting characteristics are the density of the streaking, the small bill, the small head, and the small legs. But the tale is in the tail.