"Change" would be the correct word here.
If we look at the definition:
to make the form, nature, content, future course, etc., of (something) different from what it is or from what it would be if left alone
If we think of the orange juice as an item of you're order (kind of like a conceptual container around the physical item itself), what you're actually asking is for its content to be changed ("made different").
Also, consider the definition of "exchange":
the act of giving something to someone and them giving you something else
As you haven't yet paid for the item, it isn't technically yours to give. If you were asking for them to exchange it, it would sound as if you'd already paid for it, at which point the respective monetary values of the two items would need to be considered before it were deemed a fair exchange.
However, in a restaurant context, there is a general assumption that you will be able to pay for what you order, and therefore an underlying assumption that you are the owner of whatever you have ordered, so “exchange” would sound acceptable, though it has a bit of a different feel to “change”, for those reasons.
In my view, “change” would be much more common, and “exchange” may sound a bit too formal, as well as perhaps slightly confusing, given the way it compares to a context in which you have already purchased goods, e.g., clothes, where the word “exchange” would almost always be used.