The weight savings from the small battery seems counterproductive to the functionality you want from the stuff you are putting in. Really, if you are stripping things down to that point you don't want to put in an amp, speakers, AC, passenger seats, radio or anything that isn't necessary for driving the vehicle.
(edit: rereading that, it sounds like I'm being a jerk. Sorry. What I mean to say is, putting a small battery in there should be one of the last options to cut weight. If the car is a daily driver and not a trailer queen between races, I'd say that shouldn't even be an option)
With the stuff you want, really, just put a standard battery in there. The 10 lbs isn't going to make any noticeable difference, I assure you.
That being said, Carnetix power supplies, for example have voltage monitoring and auto-shut off. On some models you can adjust this so you can be sure to cut power before it drains the battery past the point of being able to start the car.