Sharing a grandparent is easier to absorb than sharing a parent .
It's not always the case if people remember their grandparents with great fondness and find the idea of them having an illegitimate child hard to take. People can be surprising with their reactions even for things that happened many moons ago.
If the living relatives aren't into family research, don't have a tree on any of the sites and haven't done DNA, it's pretty much cold calling to contact them. At least if they're into ancestry, they'll have an awareness of 'NPEs' and may be less surprised by it.
Something else to consider is that, if they don't do DNA, you'll have to explain it to them and people don't always grasp that you don't need a test by a direct descendant to prove the case. I know a few people who have struggled with this bit in making contact with relatives.