...I don't think that's how Love Sickness works?
If the person isn't near the person they like, they die. That's how it was presented with Boa, anyway. Just spending some time around Luffy was enough to make her better. They don't have to do anything else. But, it seems like you at least have to be close to the person you like.
I honestly don't think there's anything else to it, other than MAYBE Rayleigh being a little bit shy. He just doesn't want to settle down. He's a pirate, after all. He's constantly travelling all over the world. I think HE thinks if he marries Shakky, that means his adventuring days are over. They really don't have to be, since Shakky seems rather naturally adventurous herself. But, it's a common enough fear among men, that I really don't see any need to question it, or dig any deeper. Rayleigh just associates getting married with a boring future. I'm pretty sure that's all there is to it, no matter how silly that is.
Although, I kind of have to wonder if Rayleigh assumes Shakky is just messing with him. She was SUCH a huge flirt with literally every single man she meets, I have to wonder if Rayleigh thinks this could be a prank or something, way in the back of his mind. Like she's messing with him, and stringing him along, just to prove that she can. She's not, and I'm pretty sure Rayleigh knows that. But, I could see it maybe being a issue.
Honestly, I'm not even sure if Rayleigh or Roger or any other man on Hachinosu knows how Love Sickness works, yet. Roger didn't seem to know why Shakky seemed a little under the weather beforehand. I'm not sure how many people outside of Amazon Lily actually know about Love Sickness. I could see the Kuja keeping that a secret, so that it isn't used against them. And it seems to only effect the Amazons and no one else, so knowledge of the disease might not be very wide spread. So, it's entirely possible that Rayleigh just doesn't understand how serious the situation is, yet. He doesn't realize that by avoiding Shakky, he might be killing her. Which would make for a pretty great dramatic moment on God Valley, if we get to see that.