I have done both with many "failures" but some "successes" as well. If the name is relatively unusual, I would try.

I always feel better about mailing first, then following with a phone call. Many people are (rightfully) very suspicious of strangers contacting them. I would include a brief outline of your descent (I am the daughter of XXXXX who is the daughter of xxx who is the daughter of xxxxx and XXXXX who were from YYYYY. She/he had these brothers and sisters. Then ask if they have any connection to the family or know anyone interested in the family history.

Include your phone & address

Keep it under a page. If you get no response, follow perhaps with a phone call. Remember that 3 out of 4 will likely NOT respond.

You may try first checking the county webpage to see if any possible relatives have been posting queries, even about "unrelate" lines -- they would be more likely to be interested in family history.