This is the official Apple part
It's somewhat expensive compared to the cost of a brand new shuffle. There are plenty of third-party replacements that cost less, if you search eBay, Amazon, and elsewhere on something like "shuffle cable." Some of the third-party cables have a dock and some just have a connector.
It is VERY important that the product's description says it is for the 2nd gen iPod shuffle. The 3rd and 4th gen shuffles use a cable with a different connector, so it will not work with a 2nd gen shuffle.