You are a caring man. Your empathy for and acceptance of this child will be very valuable to his life. Yes, there is a duality that you are unsure if you should continue meeting with him because of your own stammer, but I think it will allow him to see a grown man who stammers and has successfully navigated the world. Your doubts about your acceptance of his stammer are important because there is so much societal judgment attached to stutterers. He may not be nurtured by his own family. Your offering nonjudgemental attention to this child can only be beneficial.