I actually went to home depot and bought some "Thermostat" wiring, its like 33c per foot and comes with 4 wires.
I picked it because i wanted a thin cable that had a minimum of 3 wires, and was flexible...everything i could find was solid core and too rigid for what i wanted.
I honestly have no idea what gauge it is, its pretty small though, if i had to guess i'd say 20 gauge.
Something like this
It came with 4 wires, i just snip back one of the wires. As a reference, its flexibility is similar to a Cat5 network type cable, but obviously thinner...another thing i wanted to try and find but couldnt was just regular telephone wire like you would use inside to connect a phone to the wall as its flexible and small...but all the stores only had phone wire for inside the walls which was rigid.
The tube is surprisingly large, you should have space to spread the legs out a small bit to solder and it will still fit.
I had issues with taping the DS1820B to the side of the bucket, no matter how much insulation i put on(and i put on so much it was ridiculous) you could watch the sensor begin climbing the exact moment my home heater kicked in...sure my ambient was going from 66-70 and the insulated sensor was only going from 66-67, but it was still annoying and ruined what i wanted when every 90 minutes my temperature spiked up and down when the heater came on.
Then on the far end of the cable that connects to my arduino in pins, an inch or two above the end i stripped the shielding off and soldered the 4.7k resistor between data and 5v.
Im still trying to get a better way set up to have a set of 3-4+ cables that are easily interchangable and i can plug/unplug at will...right now everythings hard wired to my arduino so if something goes wrong its a pain to swap cables. Not to get onto my project tangent, but just for your information i was hoping to use a telephone/cat5 jack, and my cables have a male connector with 2 sensors each. Then adding/removing sensors is as easy as plugging unplugging a telephone wire.