sorry about this but i'm opting for brain power too!
any amount of kit good or bad can help or hinder you, it's getting the best out of what you have that is important!
i like most equipment-wise would opt for a cutting tool but , if you loose it it's worthless to you!
you have the knowledge to find cutting implements and find ways of not having to cut stuff, millions apon millions of cavemen did and survived and adapted as they saw fit! the whole point of bushcraft is to bring back that self relient world again so we can teach others!
If I had to go out my front door just now, I think I'd probably want a lighter. I know I'd be able to get enough wood by hand to have a decent fire all night, and since I haven't yet mastered fire by friction, I'd need something to get it going, of course if 1 box of matches counts as one piece of kit then I'd take that instead. Or maybe, when I think about it, maybe just a decent sleeping bag because my already built debris shelter would keep any rain/snow off.
Longer term I reckon making some sort of cutting tool would be easier to improvise from found items whilst I learned to make fire by friction so I probably would keep the lighter.