I just remembered two other "primitive" weapons that would be easy to implement and potentially more accurate than a sling, the amentum and the Swiss arrow.
I know for a fact they've been posted about on the forum before but just for those unfamiliar, the amentum is a javelin with a piece of cord or a leather thong attached that works by increasing your throwing power.
https://en.wikipedia.org/wiki/AmentumThe Swiss arrow (also known as a Dutch arrow, Scotch arrow, Yorkshire arrow or Gypsy arrow) is in some ways similar to the amentum but the cord you use is longer and doesn't stay attached to what you're throwing, in this case rather than a javelin an arrow (technically dart but basically an arrow).
https://en.wikipedia.org/wiki/Swiss_arrowBoth would be very easy to make in a survival situation I feel and would help in hunting, being that step above just a spear. The amentum was historically used for hunting, the Swiss arrow I'm less sure of and I'm not exactly sure of how powerful and so effective it would be but could most probably be used for smaller game. I've been wanting to make some Swiss arrows and try them out for myself but it's a little difficult here in the city to find the space for practice. If I can get to the Summer cottage this year, they'll be high on my "Make List".