Your district policy might say that only superintendent approval is required, NOT board approval.
But given the situation you're in, I'd go back and find your documentation in regards to the trip. If you e-mailed the Sup or had any conversations with the principal regarding the trip then I would (personally) take that as their approval if they did not deny the trip. Furthermore who made the destination selection? You? Boosters?
I know in my district the boosters make the decision on where we go, much to my chagrin. I would LOVE to take our students to Washington DC but my boosters are stuck in an Disney/Universal paradigm. Se la vis.
You may get told that New Orleans is not happening. At that point you'll need to come up with an alternative or just not take a trip at all until next year.