I've never gone in past the barb. However, I had a dog once who stuck his nose in my tackle box and came out with a snoot full. (You should have heard the pitiful noises that dog made!) Once we got him corralled, I tried the push through and snip off procedure you describe above. Given the toughness and consistency of dog nose, it was a no go and we ended up having to take him to the emergency vet who put him under and got it done. That dog never did get near a tackle box again.