I had similar circumstances, although my father knew of my existence but had never made contact - and I spent many, many years weighing up what to do. I think as long as you are prepared for the best and worst scenarios as well as a middle one, then you have covered as much as you can and you should go for it - write a letter first, it gives the person a chance to think before replying.
In my case, when I wrote the letter, the person wasn't my dad but they were kind enough to reply quickly and let me know. I did eventually track him down - heart breakingly for me he had died just 7 weeks before (one outcome I hadn't prepared for) but on a very positive note, I have found a wonderful half sister who I am incredibly close to, and she has been able to fill in many gaps including the knowledge that my father had being trying to find me too.
I am well aware that my case in unusual, but I am so glad that I finally have some answers and peace of mind now. My every best wish to you that your quest turns out equally as positively x x