I'm 99% sure this means something like "I don't want an elephant inside a boa".
Not really. I think it means something more like "I want nothing to do with...", rather than "I don't want...". It's a rejection of the entire idea, not just an expression of not wanting it. A somewhat more literal translation might be I want nothing of it -- the "of it" is like the "d'un".
Romain & Circeus have answered this well. It's about vouloir de, not just vouloir.
I'd suggest that equivalent English, for the negation, is something along the lines of your not wanting to have anything to do with it.
"Je ne veux pas d'un elephant dans un boa" means, essentially, "I want nothing to do with any elephant that is inside a boa" (or "I want nothing to do with a boa that has an elephant inside it"). One might even be inclined to add, "I don't even want to think about it."