For small game trapping, have you considered trapping with Mouse traps or Rat traps?
Trapping with Mouse Traps or Rat Traps for the non-trappers
I know that the concept of eating something from a mouse trap or rat trap is gross, but survival isn’t pretty and people will be very desperate. Better to be grossed out and alive than hungry and dead!
There are plenty of small non-mouse and non-rat animals in the forest, there are squirrels, rabbits, and chipmunks too. After a few weeks though, a mouse or rat might be a feast!
Mouse traps and Rat traps are mostly flat, you could easily fit a couple in your bug out bag or bug out kit. Keep in mind that the base is wood so after a couple uses withing a very short period of time, you’ll want to discard it and use a fresh one.
A little bait and some patience and some small animal is going to have it’s last meal. That’s sad, but it’s the circle of life and this might be the only meal you can get for a while.