If that new cable is for the current shuffle, I think it is different. If you look at the description for the Apple part at the online store
where it says "This accessory is compatible with the following," only the 3rd gen and 4the gen shuffles are listed.
This is the replacement part for the 2nd gen shuffle
You can also look for less expensive third-party products that do the same thing, at places like Amazon and eBay. Some are "docks" and some are "cables." Just be sure it specifies it's for the 2nd gen iPod shuffle.