My reference to 'delicate situations' in regards to a person trying to identify an unknown grandparent or parent - what can happen is that if a potential biological relative is contacted by a searcher, and the potential relative has no interest in helping sort out the mystery, it has happened that such a biological relative may cease all contact, remove their DNA accounts from wherever they tested, and take down their online family tree, thus making it that much harder for the searcher to solve the mystery. The Jewish DNA facebook group has advice on how to minimize this from happening, and how to be respectful when approaching potential biological relatives.
I sense from the original poster's question that he is not interested in trying to prove he is Jewish halachically, only he is wishing to learn more about his biological grandparents.
Though in a related vein - I have a maternal first cousin here in the US who has a daughter who recently married a man who is Modern Orthodox. The groom's mother demanded that my first cousin prove she is Jewish, and DNA was not an option. Luckily, my first cousin is also into genealogy, and already had gravestone photos of our strictly maternal line, going back three generations, all with Hebrew names and burial in Jewish cemeteries. My cousin later said that the rabbi from the Orthodox synagogue who performed the ceremony was embarrassed that this had happened.
And thanks to Jewishgen, AncestryDNA and New York City death certificates, I've been able to take our strictly maternal line back another 2 generations, to a woman named Sarah Shloimovitch of Lida/Lyubcha Belarus, born approximately 1820.
Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus