The answer is, there are none.
At least as far as I know, and I did search very very closely. I went to every corner, inspected every wall, jumped on top of the highest roofs, did my best to look at every angle and did not spot any chests at all. You only find those small boxes with money inside, and one of those usual "vault" secret sign which I think gave me a badass point.
Playing Gaige in a "no aiming" style requires a different mindset from the other Vault Hunters. The Ordered Chaos tree works better when using a weapon with a low Magazine Size but high Reload Rate. Generally, that means you're shifting away from automatic weapons such as SMGs and Assault Rifles that often have Magazine Sizes of 20-30+.
One other thing you'll need to force yourself to forget is reloading in between fights. Anarchy stacks based on emptying your magazine or killing an enemy, so the fewer shots you have your current magazine, the sooner you'll accumulate stacks of Anarchy.
Anarchy itself is an odd mechanic. Because it reduces Accuracy per stack, you'll actually want to use a weapon with a decent amount of Accuracy otherwise you'll be doing little damage even at close range (a la Sledge's Shotgun from the first Borderlands). Combined with the need for low Magazine Size and high Reload Rate, your best shot for a go-to weapon is anything from the pistol family. Be a revolver or a repeater, these guns have respectable Accuracy and Fire Rate, without having the relatively high Magazine Sizes you want to avoid.
With this mind, you can stack Anarchy as quickly as possible for use with your other skills. While this isn't so much a "no aiming" style, Gaige's Ordered Chaos tree puts a lower emphasis on aiming than other playstyles. What's making this hard to swallow isn't so much the skill build but the mindset involved. A lot of it run counters to what you learned in other FPSs.
P.S. If you really want tips for skill builds, I would recommend getting the Close Enough skill in the Best Friends Forever tree as soon as you invest a couple of points in the Ordered Chaos tree. With your decreased Accuracy from Anarchy stacks, the ricochet will definitely help. After more points in the Ordered Chaos tree, I would recommend coming back to the Best Friends Forever tree for The Better Half skill. As you want to empty your magazines as quickly as possible, any source of increased Fire Rate helps. In fact, The Better Half skill might actually make high Magazine Size weapons such as Assault Rifles, Machineguns, and SMGs more palatable to use.
Best Answer
In the Audio menu, try to turn off "Player Callouts". It will turn off all those little yapping and screaming (if I'm not mistaken)