I do not know all the social tricks and what have you that people doI am not sure if there are really any tricks. Establishing an earnest
relationship is usually a good start. That is, you may not get far of
you are just out to take someone's dna and run!
It looks like this second part could definitely make part of a note
you send to relatives. However, in a first communication, especially
with relatives you haven't been in touch with in a while, you might
start by explaining that you found out new info about the family,
and would like to share it.
If they seem interested, then share the possibility of being in a DNA
Thank Goodness we were born In Untied States and did not have to knowGood Luck!