Ten little Indian boys going out to dine;One choked his little self and then there were nine.

参考译文：十个印第安小孩同去吃大餐；噎死一个于是十个还剩下九。

备注：his little self相当于himself. 所以你的理解是正确的。

Seven little nigger boys chopping up sticks;One chopped himself in half, and then there were six.

七个小黑人，伐树砍枝不顺手；斧劈两半一命休，于是七个还剩六。