We have a trap used in the southern part of the province called a foot snare. It was originally designed to take coyotes and timber wolves in cubby sets. There might be some similar versions of this trap available in the States that you could use. It live traps the animal by snaring it in the foot and causes little or no damage to the target. It never took off in the north because snow fall covering the pan and snare portion of the trap would render the trap ineffective.