I have had 4 labs and none have chewed our eaten anything. If if i catch them trying . I start working on that problem right away.
Dont let them chase after any criters eather because that startes bad habites.
I had a dog get hit by a car because of that.
Shroshtr, is right about using pine cones for fetching. It keeps the dog from gettin a hard mouth.
If you try using a live pigon and the dog wants to kill it . You can make a little vest for the bird out of clouth and put thumb tacks in it to cure the problem.
When you use the vested bird make sure its alive. Pull the wing fathers off and toss it in the yard and let the dog get it.
Only do this if you have tryed it and the dog has killed the pigon.
Allways use a long check cord when you start working with live birds.
That way you make sure the dog brings the bird back to you.