Yep, they use metal bats in Little League.
Most important is that you get him the right size. A few ounces one way or the other makes a difference - there is a big difference between a 16 oz bat and a 20 oz bat.
I'm not sure how your DS is going to hit himself with a bat. I'd be more worried about him hitting another kid or vice versa. I have 2 Little Leaguers, and fortunately no one has ever been hit with a bat. We have very strict rules at our house about the use of baseball bats, and there are rules at games & practices about where the kids can and can't swing a bat.
If my boys are playing at home in the yard with friends, which they do often, they use a plastic wiffle bat and a plastic ball - that way no one gets hurt and I don't have to replace any of my neighbors' windows.