How about just ignoring it whenever possible?
I know it can be hard, but what I've done in the past is to address it at circle/group time, and to make it clear: if you see another child doing something that will hurt someone else, you may ask them to stop. If they don't, then you may tell me. Otherwise, it's not your business. You take care of you and Suzy will take care of Suzy.
And then, I just stand firm with my one-line response: That's not your business, go (play, wash your own hands, etc.) and no more eye contact, no explanations, no attention.
Taking away popsicle sticks will only work if you have a privilege or reward assigned to them. Most parents will give you an earful about rewards for not tattling, mainly because some parents do rely on the older child doing the same thing at home to keep the littler kids safe. What is 'reporting' at home--and often praised-- is tattling at school. If they feel their child is being 'penalized' because they didn't get the reward, then you will have upset parents.
If I had a child who was persistent in tattling, I would sometimes offer them a chair: "I need you to sit here until you are ready to mind your own business/let Suzy take care of herself."
With a group this size, from my experience, it is very rare that children are in such danger that tattling is warranted. I've made it clear that "if it is not happening to you, you need to let those kids figure out how they are going to solve their problem. We are all here at preschool to learn how to get along-- and we are all still learning."
Like I said, keep it short, do not give more attention than need be, and offer the tattlers who won't let it go a chair to sit in until they're ready to butt out. Usually, once the kids have gotten an " I need you to sit here until you are ready to do X" and they see I'm not running over to immediately correct the other kid, the behavior does start to diminish.
And with the children who weren't doing what was asked, I try to 'catch' them the next time, discreetly, so they don't get to skip out on following directions again. A quiet and connected (side hug) "Hey, Charlie, it's cleanup time right now. I want you to be our block guy and make our block area nice by putting them away where they belong. Come find me when you are done so I can check." A friendly squeeze, then I go off to give the child room to do what I've asked. Give the child a specific area/task and then follow up. Washing hands was a big one for my group, so I bought a soap with a nice scent and would ask to 'smell their soap'. I will bet you will come up with some clever ways to double-check on the kids who have a harder time following through with the directions given to them!