For his teeth seem for laughing round an apple. There lurk no claws behind his fingers supple;
The speaker goes from talking about the "zinc teeth" to talking about the boy's teeth. They seem made for "laughing around an apple," not for, you know, chomping their way through human flesh. Not to put too fine a point on it.
Basically, the boy's teeth aren't weapons, and he has no claws underneath his fingers either.
The speaker wants to emphasize the way in which the boy is not a violent, predatory creature, but a human being in a horrible situation. It's the weapons that are violent and evil.
Check out that word "For" at the beginning of line 9. That tells us that everything he said in stanzas 1 and 2 is because of what he's telling us here. Maybe he wants the boy to understand these weapons because the boy frankly doesn't seem cut out for all the killing he'll have to do with his rifle and bayonet. After all, dudes got no claws.
And God will grow no talons at his heels, Nor antlers through the thickness of his curls.
Not only does our speaker lack sharp teeth and claws, but God won't even help him out on that front. The Big Man Upstairs won't give the boy talons or antlers, which we imagine might come in handy in trench warfare.
Antlers and talons are sharp objects that animals use to hunt, to fight each other, and the like. You know, general bloodbath type stuff.
The point here is that boy is not like any of these animals in the slightest. His physique seems totally non-violent by nature, and we're betting our speaker thinks this kiddo isn't exactly cut out for battle. He seems too young and too innocent to understand all the violence yet. After all, he's just a boy.