First, a key point or two:
Also, what about abstracting picking pockets as simply a way to increasing barter ? (dont know if it makes sense, though)
Barter is what it costs to live and eat for a month. If your game has a trade medium (gold, bottle caps etc) it might be possible for someone to be carrying 1-barter and not notice it being stolen. Mostly, though, I tend to assume that's at least a good armload of crap. I guess you could pickpocket guns but that's really just Acting Under Fire.
The Brainer doesn't so much rely on tools as the tools either give him a noticeable advantage when using his powers and/or aren't usable by others.
Now, as to a straight out new Thief playbook, I realized a while ago why this wasn't sitting right with me. Let's take your basic D&D classes, just the real bare bones:
Fighter/the violent guy - Designed strictly for hitting and getting hit. As they level you can specialize them for sword and shield, two handed, archery etc etc.
Thief/sneaky guy - uses stealth and wits to solve problems. Has tons and tons of skills and can either be OK at all of them or good at about half. Can sneak, bluff, climb walls, pick locks, pick pockets, attack from surprise etc etc.
Priest/healer guy - Let's just say that the Hocus covers the religion and the Angel covers the healing for now.
Mage/Smart magic guy - has tons upon tons of spells. May or may not focus on one particular school. Can do lots of things really well (buff, debuff, direct attack) but takes some time to get it done.
You'll notice that all of these are so general that none of them makes an appropriate AW class. Sure, Gunlugges and Facelesses are Fighters but they're very specific, very distinct types of fighters. Arguably, Choppers, Hardholders and even Touchstones are Fighter based, too. However, all of them have a much narrower focus. They have one hook, so to speak, and go from there. The gunlugger has a big fraggin' gun. The Faceless is an unstoppable psycho killer.
So sure, start from sneaky wits using guy. But then narrow it down. What's this playbook's one gimmick. Are they so cool its a weapon? That's a battlebabe. Do they do jobs for the Guild? That's an Operator. Are they specifically focused on catching people unawares and killing them? THAT's a concept that could probably be fleshed out to fit AW. It might be a fighter or a thief in the D&D paradigm but that doesn't much matter. What matters is that they've got enough focus to merit a capitalized title, The Wraith maybe.
TL;DR - AW playbooks are more like prestige classes than basic D&D classes. Pick a specific hook or gimmick and go with it.