I can totally relate to the feeling that your angel came to you for a reason, as I am a great beliver in fate and signs. However, I can't help but think how my own heart would break forever if my Yorkie took off by accident and I never saw him again. I think I'm as attached to my dog as I am to my kids and to think I wouldn't know if he had been hit by a car or if someone took him home and was taking care of him would be a form of torture that would stay with me every day and time wouldn't heal that.
You are questioning what the right thing is to do, but I think you know that in all fairness, you have to make an attempt to find his family, or you wouldn't have posted in the first place. This shows you have a good heart.
If your little angel was really meant to stay with you, no one will come forward to claim him. Someone else in the forum said to get proof that this Yorkie belongs to whoever may come to claim him...which is very good advice.
Whatever you decide to do, I hope that this works out in your favor. I know how the little imps can steal your heart.
Honestly, I hope no one comes forward for him, because he is obviously good for you and your family.
Good luck in whatever you decide.