There is no problem feeding koi worms if they'll eat 'em. I truly don't think a koi would contract anything from a worm. In fact, why wouldn't you just feed them critters in general, like mosquitos, flies, etc. that are all considered to harbor diseases. At least you'd give those koi more variety. LOL!
I've tried feeding 'em worms, but my koi won't eat them. But I really don't think you'll find the koi will get anything from eating any of those things.
Most koi get diseases and issues from poor water quality. The water itself harbors lots of bacterias, fungus', parasites, etc. If a koi has a weakened system in any way or a wound, etc. Then these beasts get into 'em and wreak havoc. Of course, there are things like viruses that one fish can give to another, etc. But I think you'll be hard-pressed to find a koi dying from eating worms such as you describe.
What do you plan on doing with the fish when you are done with your experiment? How are you filtering these kiddie pools (poor filtration will surely kill them), plus a kiddie pool is very shallow and gets hot very quickly in these temps that will warm up, I can assure you that will kill a fish faster than any worm.