Will cancelling adobe stock get rid of generative ai?

You mean the stand alone Firefly Generative AI program? Don't use it, if you do your creations. There is no way to ask for a product that does not include some generative A

Generative AI tools have been incorporated in numerous Adobe products, including Photoshop and Lightroom, among others. It's not possible to remove those tools from within the software; however they're usually labeled as such so you know when you're using AI. 

Simply not possible to the best of my knowledge.