The screener kept insisting that I needed to open the container so she could hold that little test strip over it. I held firm and explained that opening the container would cause the milk to spoil and the container wasn't resealable.
They can make you open a container you filled yourself, like a baby bottle but if it's factory sealed, they're not supposed to. Wish I could give you a link but email them for confirmation so you can print it up.
Another solution I read I think here, ages ago, is to freeze a bag of grapes (or similar, freezable, snack food) and put it in a bag. This is your "ice" pack but then it thaws and you can eat your snack!
Not sure how practical that is in the OP's case but if it helps someone out, especially on a shortish flight...