I did precisely this and got one reply, from which countless further progress has been made. As background, my family roots are in Hull, but not forever (as I once thought) but only since 3 brothers moved there from Norfolk in the 1840s.
I started off by apologising in case the letter was not relevant to the reader and then asked if they (like me) thought that their ancestors had all come from Hull and pointed out the Norfolk link, stated how far back I had taken the family history and then offered to share it with them if it turned out they were from the same tree. I gave what information I had at the time, going right up to my own father and wrapped up by saying that if we were related and they had any photos of dead ancestors, that I would love to make copies of these pictures at my own expense.
I think the key is to get enough information in front of them to let them work out for themselves if we are related, but not so much that they don't read it. I am coming to the conclusion that a traditional family tree outline is probably best to use for this purpose.
My current dilemma arises because I now have much more information and could probably get a better hit rate by sharing it in another mailing but am uncertain whether to risk another mass mailing again less than 12 months after the first. I'll probably bumble along for a few more months to find out a bit more for myself before going for another mailing.
A letter is pretty harmless. If they get upset, they can throw it away. Apparently one of my recipients, the widow of my dad's cousin got rather upset but was mollified when she heard my dad's cousin had had the same letter. Be chatty and amusing if that is your style and include SAE. Good luck.
