It's only a slight underbite? Then why worry? What will fattening up your lip do for your teeth? If your underbite is enough to affect your appearance when you're not flashing all of the pearly-whites you can, then it's not a slight underbite.
I work in a dental lab where we make all manner of dentures, splints, mouthguards, etc. We've made dentures for overbites, underbites, and crossbites that, when you're just seeing the teeth, look pretty frikkin' bad. But when the patient puts them in, you'd be hard-pressed to tell.
So just how "slight" is this overbite? If it's not affecting your ability to chew food and doesn't have you walking around looking like a bulldog trying to pick a fight, then it's probably something you shouldn't waste your money on.