FiveTen stealth rubber is the grippiest rubber on earth, or so they claim. I have the soles on a couple of pairs of shoes and I would have to agree. It's unbelievable how well they grip, you almost feel like you're glued to the ground. Unfortunately on the shoes I've tried the quality isn't very good or very comfortable, but it's almost worth the discomfort for the grip they provide.
I've only found one lightweight hiking boot that uses stealth rubber in their regular hiking boot, the Vasque Catalyst Mid. It's the best of both worlds, a comfortable shoe with great sole. The rubber does wear out faster than a normal sole, but that's the price you pay for friction.
You can also look for approach shoes, most climbing shoe brands have one. They are basically rock climbing rubber soles on a light weight non-rockclimbing shoe (no boots). They're made to wear while hiking to a climbing spot, where you need a comfortable shoe to walk longer distances in, but also grippy soles to do scrambling. Doesn't sound like you're going to using these for hiking, so don't know if this'll work for you.