I think that the larger mouse/rat trap would certainly work on various squrrels, Rabbits might be stretching it a little. My grandparents used to use these to keep the chipmunks out of their wood pile. The "camouflage" technique you suggested wouldnt be needed. You could sprinkle dirt,small twigs and leaves around it to mask its shape easy enough. Howevever, to be effective you might need to carry several of them and in my case I would think that to be too much bulk and added weight for my pack. Might work for your intended "kit" though IMHO.