If your cat is going to be outdoors, which is clearly the case, since the subject is catching birds, I wouldn't recommend the claw covers. Any cat outdoors may encounter a situation where the claws might be necessary.
Bells on the collar might help but cats are amazing adapters. I'll be you'll find that your little darling will learn to stalk without ringing the bell.
In time, your cat will probably grow out of it. I took in a feral cat years ago, and just lost her, probably to a fox, less than a year ago. I won't go into detail about her because I've done that elsewhere in this forum, but on-topic in this thread is how she got her name -- Bird.
She was a tiny little kitty, and the most agile cat I've ever had. She could cross from one tree to another by walking to the end of a branch as it bent over, crossing onto the branches of another tree.
Before I took her in, she was sitting on my lap outside our ambulance station, as I was talking to our landlord, the man we rented the station building from, who lived next door. This was in South Texas, near Mexico, and he had several hummingbird feeders up in a large tree. He had it set up so that he could lower them with pulleys to refill them, etc.
At the time that we were talking, there were six different varieties of hummingbirds in his feeders, he said. I had to accept his word for it because they were tiny birds high in a tree, and I could barely see them, let alone determine subspecies.
Bird seemed to be paying no attention whatsoever. In time, our neighbor went back inside his house and I went into the station. Not long after, I came out to find this kitty bouncing something around in the driveway.
It was a hummingbird. She had gone up and got herself one. She also got a name.
Even after I took her into the house, she was an avid hunter, killing and eating all manner of birds and rodents. But after a few years, she began bringing them in alive and unharmed. She would come in the cat door, meowing loudly so that the other cats could see what she had brought them, drop whatever it was on the floor, and prance proudly off, as if her job was done.
I would then rescue the creature and bring it back outside, but I tried to do that when Bird wasn't watching so as not to hurt her feelings.
Over the years, she had brought in countless birds and rodents, a snake, a baby snapping turtle, frogs, and even a live bat (neither she or the bat were harmed). She would also leave gifts outside our bedroom door, which included dirt clods, empty cigarette wrappers that she must have dug out of someone's trash, leaves, branches, etc.
Her goal was to bring the outside inside, apparently.
