We don't have synonyms for say cheese yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are rat cheese and sage cheese.
(v) :
(idiomatic, chiefly imperative) To smile for a photograph by saying the word "cheese" (the vowel of which, when pronounced as is usual in English, forces a somewhat smile-shaped mouth).
(v) :
(idiomatic, chiefly imperative) To smile for a photograph by saying the word "cheese" (the vowel of which, when pronounced as is usual in English, forces a somewhat smile-shaped mouth).