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As a kid, I used to set snares for cottontail rabbits. I probably caught well over 200 in the space of 3-4 years. A much better material for snares than paracord is picture wire. Picture wire is the thin braided wire used to hang heavy pictures on a wall. it is available in most hardware stores and big box stores like lowes or home Depot and is not very expensive. The big advantage of picture wire is that it holds it shape well when not bearing a load. rabbits will either sense that they are caught and sit patiently until they hear the approach of a predator (you), or will immediately struggle and tighten the noose and strangle.