Don't want to rain on you idea BUT...
While the AGFC has no regulations that prevent the snaring of Rabbit or Squirrel specifically during the trapping season, there is a deer-lock requirement for any land snare set more than 20ft from a permanent water source. That deer-lock prevents a snare from closing less than 2 1/2" in diameter. That requirement all but ensures bunnies and tree-rats would escape...AND even if held, you would need to run the line at a minimum of twice in 24 hours to keep Yotes, Cats, Fox, Coons and Raptors from stealing your catch...