In Chrome/Chromium you can do this in the developer console.
- Bring up the developer console by either ctrl-shift-j or Menu->Tools->Developer Console.
- Within the developer console browse to the Sources tab.
- In the top-left corner of this tab is an icon with a disclosure triangle. Click on it.
- Browse to <domain>→css→<css file you want to eliminate>
- Highlight all of the text and hit delete.
- Rinse and repeat for each stylesheet you want to disable.