That sounds like a good solution.
From a general perspective, there should be no problem telling someone "I don't use FB (or whatever) this way. I'm sorry." A reasonable person will accept that. Someone who doesn't is showing that they don't respect boundaries.
I agree! I am in the camp of "if I don't know you, I don't friend you" The only exception to that rule was the partner of a friend from HS, who friended me. While I've never met her, her being with my friend is enough for me. We don't do more than like or comment on each other's posts, but that's fine.
Everyone else I either knew from school or some other point in my life, or is family. And I've actually hesitated and NOT friended the kids of my own cousins, since I've never met them, and thought well, maybe they might think its weird, or someone else might think it inappropriate. Even though I know people who friend anyone and everyone they ever came into contact with!