I apologize if one already exists.
So far, the only one I am aware of is for The Lion King.
There is this CD, released in the UK, simply called "The Lion King Sing Along"
http://s-tlk.org/tlk/media/cd/tlk-singalong_cover.png
Unfortunately, I do not know the stock number, but Discogs lists the cassette tape version here.
I do have a friend who owns a copy of it, so I could potentially have them scan the whole thing since it's super obscure now. Only the front art is easy to find.
It's super, super, super hard to find now. It seems to have been replaced by this monstrosity which uses crappy cover versions.

Sadly, the 1994 CD only has five songs (both vocal+instrumental versions), but they are absolutely genuine, not re-recorded garbage, and they have almost no backing vocals (Be Prepared, for example, still has some of the grunts, but that's to be expected. Circle of Life still starts with Carmen Twillie's solo but then once the music starts the vocals go away, it's just some of the African chanting)
However, speaking of The Lion King, the promotional single for Elton John's version of Can You Feel the Love Tonight (IMO much superior to the one in the movie) has an official instrumental version as well, plus another score track that isn't on the main soundtrack.
That one isn't hard to find at all. Some more info on the Discogs page here. (And hey, it plays in the end credits, so I can call it legit Disney movie music
It is my understanding that most of the "Disney Karaoke Series" is just cheap cover versions, the number one giveaway is that the singers are not the real singers from the movie. And why would they use official backing tracks with crappy singers? I bought a copy of the Frozen karaoke CD recently as it was on sale, almost wanted to throw the thing out a window after hearing about 30 seconds of that garbage.
(Oh, the two-disc special edition soundtrack has the proper instrumental of Let It Go, I guess that's worth mentioning as well)
I would really love to know if there are any other obscure releases out there with instrumental versions from other Disney classics, like The Little Mermaid, Beauty and the Beast, Aladdin, and so on. I'd also really love an instrumental of I'll Make a Man Out of You. That's my most sought after.
A friend of mine alerted me to this CD, Disney Karaoke Volume 3. While the instrumental of I'll Make a Man Out of You does sound pretty darn close to the original, one thing that immediately gets my attention is that they put in some sort of a trombone or other low brass instrument playing what would have been Donny Osmond's sung part. So it's not so much an instrumental/backing track as it is "here's an instrumental with some dude playing the vocal part instead of singing it."



