You are worried about putting them too close to the dinner table? I assume you mean where your horses eat not where you eat, right?
I think you are WAY over thinking this.
You can sprinkle them in stalls even.
Every person I know uses them in a similar manner to how I use them. I have one friend who also sprinkles them in her stalls. One friend who sprinkles them in their run in (I do not have a run in and my stalls are in and out with most manure being done outside, or I would sprinkle them in the stalls too.)
They will do not harm to your horses. They can be sprinkled anywhere you want to sprinkle them. I suggest you follow the directions that come with them for the best results.