Brief Summary
Currently the only way to selectively delete a site's application data/cache is by going into "Settings", "Privacy", and clicking "Manage..." under "Cookies and website data". Then you can find and delete specific sites' data.
I'd propose a quicker/simpler way to do this on a per-site basis.
Details:
Chrome and Firefox have similar shortcuts for deleting the active website's data/cache.
Chrome: (from the toolbar)

Firefox: (from the developer tools)

I think the simplest option would be for Orion to support two functions:
- Clear this site's cache
- Clear this site's data (including cookies, local storage, databases, etc.)
User's could apply these functions to programmable buttons if they like, but I don't neccesarily "need" specific buttons for this.
I only suggest they be separate functions because that is what I'm used to; perhaps they each item of data could be selectable for deletion?