So, as Celestia stealthily sings her way to the kitchens, what tune would you use for her lyrics?

It felt Gilbert and Sullivan to me. Maybe "With Cat-like Tread", from Pirates of Penzance.

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I say 'you are my sunshine, my only sunshine'

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If that wasn't against site rules, I'd totally use that. Have Celestia dancing down the halls, bellowing at full volume about how sneaky she's being and how she'd hear a fly's foot falls.

Pink Panther or Mission Impossible.

Rewrite This Day Aria to be about cakes, cookies, and pudding?

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Yes! But also add the cider song chorus (aka the part where they say cider like crazy) as a minor chorus so it also includes drinks

Bret Roberts - Sweet Cake

This one (WARNING, not for the faint of heart)

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You got to love Richard

7073657 "Petey's King of France" from Mickey, Donald, Goofy: Three Musketeers