Yeah, as long as he's not choking now he's likely not going to. As noted above though the bone could hurt his stomach, especially since he's a smaller dog. He's not gonna go out and shit the bone out any time today. What you need to do is watch him like a hawk when he's shitting to make sure there's no blood in his poop. If there is, you need to rush him to the vet. Also, if he starts acting like he's in pain for no reason, or is suddenly listless and not active, rush him to the vet.
In the future, UNDER NO CIRCUMSTANCES GIVE OR LET YOUR DOG GET A BONE. Make sure other family members know this too.