1. If you are in the US, Cubbiecakes is technically right. Transposing the song to another key is NOT a copyright infringement (and yes, an accomplished accompanist should be able to do that on sight, although it's usually considered rude to show up for something like an open cabaret and hand an unknown accompanist who has limited rehearsal time with you the music in the wrong key without prior notice) but transcribing the introduction section and
putting it into written notation is (again *technically*) not fair use according to copyright. Playing it by ear like Imzadi suggests would be much less of a violation (if any - it's a bit of a legal grey area at the moment.) But I assume the cabaret is providing an accompanist for the entire evening? Again, it's not really reasonable to show up to work with an unknown accompanist and expect them to play a chunk of your piece by ear. If you get to bring your own accompanist, that would be a different story.
1.5
https://nafme.org/my-classroom/copyright/copyright-arranging-adapting-transcribing/ This is from the music teacher's national organization. You'll notice we are being told as a profession that transcribing (listening to a piece and writing down exactly what is happening musically) is something that needs permission from the copyright holder.
2. On the one hand, copyright lawyers aren't generally hanging out at local gigs looking to sue people. On the other hand, Disney is one of the most zealous defenders of their copyrights there is. It's possible that if the whole thing is a Disney cabaret, the people in charge may be requiring you to provide legal sheet music. Just like when your kids go to solo festivals in various states, they're not allowed to bring in (illegal) copies of their music, many talent shows do the same thing to CYA as far as copyright.
3. Writing off the intro part temporarily, LuvBunnies is totally right. Musicnotes.com is a fantastic place to purchase transposable sheet music online. Not all of their pieces are transposable, but a LOT are.
4. If you are willing to share the name of the piece, I would guess there are a number of us musicians here who might be able to get our hands on a (legal) version with the introduction. We have ways.
5. If musicnotes doesn't pan out, Imzadi has some great suggestions on finding someone capable of transcribing your intro and transposing your piece, but you may find your local college pretty well cleared out of musicians this time of year.
6. You can PM me if you want. I may be able to help you out. 20+ years directing bands, choirs, musical theater and teaching voice lessons.
What you need may be on my shelf!