Banksy says you can do it. Shepard Fairey prefers using celebrities. In fact most graffiti artists are all about altering logos and commercial to make a statement. Richard Prince may be the king of this, as seen in his now infamous instagram art show where prints sold for $90,000 a piece (though he's been doing it for years).
There is a technical reading of the law that makes a case if you alter something 30% or 50% or even 5% and you are good to go.
And these readings may be correct. They may be technically correct at least, which is the best form of correct.
If you used the Disney logo, altered it, and made your own logo from it, there is a decent chance you can win a lawsuit against Disney.
But there is a 100% chance they will sue. Especially with Trademarks, they HAVE to sue to retain it.
And even if you're right, morally, legally, ethically... you still have to come up with the money to fight a lawsuit from a company that has roughly infinity dollars.
This is the question people don't ask themselves enough, especially when they are starting out and building their brand. Is it worth the agonizing stress and financial ruin that will come with being sued by Disney, or is it worth it to change to another company, or create a new product and avoid it all together?
Maybe it's worth it to you. I don't know. I can't answer that. Just know, that it's certainly something you will have to deal with, especially if you build your brand around a doctored logo from another company's brand.