Context reaction : Exclude specific block?
It might not be overkill to duplicate the context if it works ;)

Context is often used with Delta to provide layout and theme adjustments for internal pages. After setting up a few Delta layouts you will be able to specify a Context/Delta reaction and switch the applied Delta template for your Shop-product page.

Take a look at this decent Delta+Context tutorial. Good luck!

EDIT: If you're not already committed to a theme, the Omega theme has some incredible integration with Context/Delta - intro tutorial here.