There were several boxes that may have been in use in 1923, the photo below shows 2 that were in use in the 1920s. The photo is from my book, "Cracker Jack, the Unauthorized Guide to Advertising Collectibles", page 6. The prizes in the boxes were typically the pot metal charms. Typical examples are in my book, "Cracker Jack Toys", pages 40-60+. Most were pot metal, but there were probably earlier paper and metal prizes as Cracker Jack used earlier prizes for many years.
I believe Woolworth, at the time was more into dry goods (i.e. non-perishable, non-food items, so the "pitch" would be appropriate (trying to get them to carry a packaged food line), but may not have been successful.
Let me think some more on this and see if I come up with other info.