Practice may be available. California, for example, has a small number of no limit, no season critters such as english sparrows. carp, and wild pigs [check the regs near you].

Small critters once cleaned can be cooked whole or dried/ ground / powdered and cooked into "stoup." A few wild edible plants could help palatability.

I think the lowest tech allowed harvest method is by bow.

Biggest issue for me is finding clean environments from which to legally practice such harvests.

Each prey has its own habits, diseases, etcetera that the reponsible harvester should learn. The internet should provide what you need.