EDIT (Sort Of; See Below): This is something of a thought progression, and the statements made in the beginning are not final stances, so do not be offended if I disagree initially. I did some "research," which I've included in the edit at the bottom. At the same time, prepare for a lot of close scrutiny and doubt.
Well, a level 20 Cloak of Shadows has -72%. Normally this would be more than enough, but this is halved against champions/bosses (and presumably uniques and super uniques if it is halved against champions). So at level 20, this is -36%. That's certainly not bad. But then you also have to consider the levels of act end bosses, especially Baal, since their level is used in the to-hit equation, thus reducing your chance of hitting them if you're lower level (which is likely unless you're going back to a mode you have already beaten).
Anyway, so then you can compare Claw Mastery to some of the bonuses to attack rating from weapons. Claw Mastery, in my honest opinion, is not worth the damage bonus. Even at level 20 it only adds 111%. It's better to simply get a weapon with a powerful modifier. So then we inspect the attack rating: 220% at level 20. It gets 30% at level 1 and 10% each level thereafter. Unfortunately for Claw Mastery, there are weapons with 300% attack rating bonuses (effectively quadrupling your attack rating). The cost is that they're two-handed, thus halving your damage. Of course, they quadruple your chance of hitting at the expense of only your weapon and claw/shield slot, meaning you're still doing more damage because you're hitting much more often.
In this, I could see a claw-based build being viable, but I think that a non-claw build would be better in the end (so while the claw build might be the "budget" version, the optimal, "rich" build probably shouldn't use a claw).
Also, where you only have 110 skill points total (if you get to level 99, which most people do not), maximizing the benefits of Claw Mastery will cost you twenty of those, nineteen more than other Blade Fury builds. Of course, if you do max out Claw Mastery, you'll get a little bit more attack rating from skill bonuses, making it comparable in attack rating with a 300% AR runeword. I just personally don't see how that's worth 19 skill points though.
EDIT (Not Really, But After Looking Up Some Information): Apparently enemy defense scores simply... suck. Even Uber Baal has only 3150. I'm still not sure how this interacts with the number of players in the game or how his level influences the hit ratio. Anyway, the point in this is that, while I still think it's not worth putting a bunch of points into Claw Mastery, both versions would be viable in PvM (as far as the ability to hit enemies goes). As a matter of fact, simply with level 20 Cloak of Shadows, Uber Baal suddenly has a pathetic 2016 defense. This actually makes dual claws rather tempting for the claw block (since it can block some spells) since it appears a claw character can work. Even with a single point of Claw Mastery, you can easily get that to level 20 or so (9 grand charms, 3 from the hellfire torch, 1 from annihilus, 2 from bul-kathos' wedding band, 2 from mara's kaleidoscope, etc.). So you have 200% AR bonus (each point of dexterity adds 12 AR or so), and some bonuses from those very same pieces of equipment to dexterity (60 AR from Mara's, 120-240 from the Torch and Anni, etc.).
So you have a "free" (since these pieces of equipment are pretty much necessary for the life leech, resistances, etc.) 300-540 attack rating just from the named items.
So, yes, claws might be the path to pursue, it seems. I think Chaos and Bartuc's might be a good set-up, with Chaos in the hand for Blade Fury's damage, and with Bartuc's in the other. This gives you a good amount of open wounds, magic damage (to make up for the pretty crappy damage claws deal), life leech, skills, and a 20% bonus to attack rating.
So, attack rating without other factors: 648-936. This doesn't even account for the base dexterity and attack rating, and it uses an approximation on Claw Mastery at 200% since the rest of the equipment isn't set in stone yet.
EDIT 2 (Not Really Yet Again): Without putting a lot of points into dexterity (which doesn't help the block ratio with claws), the attack rating still sucks... Even with 300% AR from a weapon it would probably suck quite a bit. There are still factors that could be added in, but it would require quite a bit more to make this viable. And it still needs Crushing Blow as well (vital to this, even though ranged weapons suffer a penalty on crushing blow - 1/16 of the target's health against Champions/Uniques/Bosses).
At the same time, all the bonuses to skills would help Cloak of Shadows quite a bit, so I'm going to take a quick look at that: Okay, so this caps out at level 28 as far as reducing an enemy's defense goes. It has -95% at that point (-47.5% against Champions/Uniques/Bosses). So, looking again at Uber Baal, his defense becomes 1653.75. It's still fairly far away from the attack rating this character has without additional points of dexterity (which, again, only boost damage and defense a little).
EDIT 3 (Another Fake Edit): Using fairly standard end-game gear, Claw Mastery, with 1 hard point in it, returns 250% Attack Rating. So this boosts our figures a little bit, but still not enough to make it very effective without more hard points of dexterity. Attack rating becomes: 756-1092. Now, admittedly, if you added on 190% more attack rating (19 more hard points in Claw Mastery), I don't doubt that it would become viable. The problem with this, then, is that Cloak of Shadows lasts for 35 seconds. Then you have to re-cast it. And in the meantime, your Blade Fury is single-target (at a time, at least, since I do understand that once an enemy is downed, any still-flying blades will hit whatever was behind him). This means crowd control is weak to nonexistent. And, while this isn't so much of an issue against bosses, Baal does have a clone and tentacles, and while you shoot down those tentacles, he's going to keep on attacking.
Of course, I've been using Uber Baal's defense as a target number, but I don't ever expect this character to be able to kill the Ubers. It simply wouldn't happen. Its complete lack of effective crowd control, and the short duration of Cloak of Shadows mean it would die as fast as a Tal Rasha-wearing Sorceress in her low 70s using fire spells.
Conclusion: This build is not as simple as it seems, even with Claw Mastery and a ton of items to boost Claw Mastery (though the grand charms and the like are optimal anyway because they boost Venom and Cloak of Shadows and Fade anyway). As such, it isn't quite the budget character that it seems to be at first (at least as far as conquering Hell mode goes; it's perfectly viable in the first two modes, and even likely the first two acts of Hell solo).
REAL EDIT: Oh, even at level 41, Cloak of Shadows has a 48 second duration (compared to the 600 second/10 minute duration of Fade, which is amazing...).
REAL EDIT 2: I just ran it all through a damage calculator, and if you could manage to make it hit reliably, it's capable of dealing a little over 2,000 damage per hit (counting Venom, the magic damage of Chaos, etc.) but that uses an ethereal War Fist, and I'm not sure if ethereal is compatible with claw blocking. If not, it loses about 500 damage. And that's not counting the fact that most bosses will resist most of the poison damage. So, in short, its damage isn't horrible, but it's not amazing (and 19 more hard points of Claw Mastery honestly only adds about 100-200 damage). This is using Fortitude and a Phoenix Shield, too, which means that skill points decrease, so it's actually an overestimation. In short: damage is worthless (really, entirely worthless). This character only reliably deals 1500 damage (since I do believe that claw blocking ruins durability), and that can be reduced to about 1000-1300 once you account for 4 less points in Venom and Claw Mastery). Also, this severely reduces attack rating (60% less without Bartuc's and those 4 points of Claw Mastery). So, basically, decent damage (not even good or great damage) comes at the expense of accuracy.
So, short version: you have to focus on crushing blow. It's the only way to make this viable. And you have to make sure you have a good amount of attack rating, or even more -X% target's defense (aside from Cloak of Shadows, so you can exceed the 47.5% it offers).