Synonym of "s--t eating grin" suitable for polite company

Can anyone think of a synonym for "shit eating grin" that would be usable in polite company?

This definition from the OED captures the meaning I'm looking for perfectly:

A broad grin expressing uncontrollable delight or (self-)satisfaction, esp. characterized by awareness of having got away with something normally considered outrageous or improper.

As pointed out in this Metafiler comment, an important nuance is that this sort of grin is uncontrollable.

One synonym for "shit-eating" is smug:

looking or feeling too pleased about something you have done or achieved

So you can say that someone has a "smug grin" or a "smug look on their face". It still has the negative connotation of "shit-eating grin", but is suitable for polite company.

A related idiom is that one can look like the cat that got the cream:

if someone looks like the cat that got the cream, they annoy other people by looking very pleased with themselves because of something good that they have done

It's a little obscure but…

...grin like a Cheshire cat.

fits the bill.

You could use the word:

smirk
verb (used without object)
1. to smile in an affected, smug, or offensively familiar way.

It's a bit more wordy, but I suggest:

You look like the cat that ate the canary.

A big, cheesy grin

Cheesy, as in "Say cheese!" but also as in,

adj., cheap, unpleasant, or blatantly inauthentic.