I would be tempted to disconnect the existing battery and to hook this device to the leads and see how it doe on its own. You need to be careful to avoid shorts and sparks, lead-acid batteries produce hydrogen gas that can burn or explode, but it is pretty simple. Most battery leads can be worked with a 5/18" nut driver.

While the terminals are off I would go ahead and clean the posts and terminals. A wire brush is standard but I've found a green scrubbie from the kitchen to be easy and effective. Once you use it on a lead terminal post I wouldn't use it in the kitchen. And wash your hands. Once clean a little petroleum jelly will help keep the terminals free of corrosion.