Dynamically change the default browser?
ControlPlane would be a good option for you. It has the ability to define contexts based on specific criteria (if plugged in to power or not), and perform many different actions based on those criteria (including switching your default browser).

Here's a screenshot of ControlPlane's Evidence Sources window and DefaulBrowser Action settings:



I use ControlPlane for a lot of things, like switching my Network Location based on the wifi network I'm connected to, and switching my default browser based on my Network Location. It's a really powerful little utility.