You write to him and say, "Hi, it's Mary Smith. Are you the same Friedrick Hinkelbungarten that I used to know in Poughkeepsie in 1998? We used to play jazz and send helium balloons up at night." In other words, do what you would do with anyone else who might be from your past, briefly name something he would remember. Then if he responds positively, say "I'm getting in touch to let you know that our relationship, short though it was, produced a son. He's the best thing that ever happened in my life, and I don't have any intention of making a claim on you, but I did think you should know about him, [etc. etc.]"
You don't put the second set of information out there until you get a clear confirmation that old Friedrick is really the same guy, of course.
For what it's worth, I was looking in the White Pages for the phone number of my son's kindergarten teacher, and got not one, not two, but three women with the same first and last name (and it is not a run-of-the-mill name, either), only with different middle initials, all in the same town. Maybe they are all family members and would know each other if I called one and asked if she had been a kindergarten teacher to my son, but it was kind of amazing that in such a small area we would have three of them. I hope the guy you found is the right guy.