Learn English – “Figment” other than in “figment of the imagination”

The reason that people are asked to say "Cheese" is because the "ee" sound brings the speaker's lips up into a smile, while the "se" sound at the end brings their teeth together to form a smile.

Any similar word construct works, such as "flea's knees", "burt's bees", or even "smile please!"

Other words that just have an "ee" or an "s" sound at the end can also be used, though are less common. One example I can think of is in the video game Earthbound, a magical camera man asks you to say "Fuzzy Pickles!" Which is also funny enough to make you smile anyway.

The short answer then is, "whatever works, works".

See this question and answer for further reference.