If the opera piece being performed is in public domain, then you don’t have to worry about those rights, and in this case, the performing rights are done by the chef of which you should have him signed off anyway as part of the production. Not being an entertainment lawyer, I would think you are fine. So if I had an actor sing Amazing Grace in a scene, I would be fine. The published song in the public domain, but you are creating a new performance of it. Where things get tricky is when there is a new arrangement to a public domain song that now has a rights that need to be cleared.
I like the idea of what you’re going after, but you may have to search a little deeper to see if you can find a performance of the same piece in the public domain, or see how much it would cost. Rights fees can change based on where it’s played, country, etc. And if 10 seconds, it may not be that much and worth considering.
Michael