Thanks for replying and for your advice.
Do you have any recommendations on starting such a letter and should I put anything on the envelope stating that it's genealogy research?
Currently, it would only be one letter as the person is not just a surname match but also has the first name as a niece of my grandfather. At some point if I were to have a lager list of possible relatives, I wouldn't mind spending the postage just knowing that I made the attempt. While I am pretty new to genealogy, I try to be an optimistic person in regards to my research. There's every possibility that I may never get a reply even if they are part of the family. There could be a chance that they may not see the letter because they are elderly or ill and that one of their children may see it.