The best way I found to fasten hardware cloth to wood is lath screws. I use #8 3/4" Teks lath screws from Home Depot, $5.24 for 200 of them. I see no way that any predator could pull a 3/4" screw out of wood. Might could happen, I just don't see how. This is so much faster than nailing in small fencing staples (and less frustrating too), and much more secure than the staple gun route.