I find your proposition correct too... Here, "while" more or less means "when", so your sentence could mean "when/every time you smiles"; the simple past refers to the complete, finite action of smiling. If you use the progressive form, it's as if you had taken a snapshot of the person as s/he is smiling, it doesn't refer to the total action.
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My question's this:
'while you smiled' is okay?Yes, but I find it a little anomalous. In fact, I like your direct translation better. How many times did you smile, hiding that sadness? I might also have said How many times have you smiled, hiding that sadness?
CJ