How can I get a bone for a bone shiv without getting lucky with a drop?

From my experience, the normal club is the best way to harvest an animals prior to having the bone shiv. It will yield little meat, no hides, but 1-5 Bones if you finish harvesting the animal. From there, craft a bone shiv and you are good to go to harvest your next animal. Keep the bones around since you cannot repair your bone shiv.

In A15, you can use a stone axe to swing at a corpse. Once you've collected all of the meat from it and it degrades to its final form, it will start yielding bones.

In general, the axe is better for harvesting meat than the club. The bone shiv is better than the axe, and the hunting knife is best once you can craft it.