Pete the Cat And His White Shoes sounds great. He steps in strawberries, blueberries, and mud, so if you don't find a cute shoe, maybe a piece of his shoelace? Or a pretend strawberry?
There's also a "pete the cat and his school shoes". He visits the library and the cafeteria so maybe you could get a pretend library card or a bookmark that "pete found while he was in the library."
If you do Pete the Cat, bring your pretend guitar! He carrys a guitar and sings a little in both books.
I just looked thru my son's bookshelf and it's hard to do the 'acting it out' AND a trinket.
Maybe "Don't let the pigeon drive the Bus" by Mo willems (give a bird feather to each child).
Maybe you should figure out your cheap trinket FIRST, then search books with that trinket. ie: a bead, an eraser; THEN go search your library for subject or keyword "eraser"
@Kim's idea: There's a book "There was an old lady who swallowed a SHELL." I think they sell shells at the $1 store.
@Dawn's idea: If you read Corduroy, you could give each child a button. YELLOW button I believe.