Word of advice: Don't buy USB cables (or any connection cables) at Best Buy or most other brick and mortar retailers. The markup is extremely high. (Connection cables are a great example of something that's best purchased online.)
You're looking not for a standard USB cable like you'd use for a printer, but for an "extension cord," so that you could move that printer 10 feet farther from the computer--something like that. Don't worry, those are actually pretty easy to find if you search for a "USB extension cable."
Here are two that would work:
Name Brand (Belkin): http://www.newegg.com/Product/Product.aspx?Item=N82E16812107286
Even after shipping, you come out way ahead.
As for repairing the original cable in question, I agree that soldering and heat-shrinking each individual conductor is the way to go. It would be the most reliable way to do it, even though it won't exactly be pretty or elegant. (I've done this to extend a run of cat5 cable before--just have to be careful not to untwist the pairs too much.)
So really, just order the new one for $2.99 + shipping.