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You could have them in a basket/tray at the door- as people come in, they get a pom pom and program? Or on every seat could work. I'm having a hard time picturing what you mean (I'm thinking of the little cheering pom poms on sticks you see at sporting events) but I think one per guest would be ok. Of course, the guests have to hold them throughout the ceremony...Hmm.
I'm guessing you're wanting to get some fun pictures with the pom poms in the air as you are walking back up the aisle. Is there any way to do this as part of a "grand exit" after the entire ceremony is over? That might make the logistics a little easier.
Oh ok, I get it now! I think the timeline sounds fine. I was assuming separate venues, my bad!
To be honest, I bet it would make for some cute pictures, but it seems like a lot of hassle. Other than the cleaning up and the issues you mentioned of where to put them, how will people know to throw them? What if you take a pom pom to the eye? I guess I don't have much helpful feedback other than that I would reconsider.
I don't really have anything nice to say. OP, just keep in mind all ideas found on Pintrest aren't necessarily awesome. Having things thrown at you after getting married is certainly not a requirement. This seems like a waste of money.