Oh, I'm not the expert but I do know that amp ratings are not proportional to the wire gauge. 8 awg is good for 24 amps whereas 4 awg is good for 60 amps.
In your case, I would be concerned with routing the cable and, more importantly, making a good connection of each end.
The little extra wire with the connector is not a big deal. I cut it close to the main cable and, if I remember right, stuffed it into the lug prior to soldering the end. That cable has something to do with the alarm system so you have to properly deal with it.