I think you are asking about the iPod RESET Utility. There is no 64-bit version.
A "Restore" is normally done using iTunes, from the shuffle's Settings screen. This "Reset" utility is only for the 1st and 2nd gen shuffle, for use in a particular unusual case where the computer (Windows) sees the iPod, but iTunes does not. If iTunes does not see the iPod, it's not possible to use the Restore button in iTunes. But since the computer still sees the shuffle as a USB device, you can try that utility. When those older shuffle models were sold as new, there was no need for a 64-bit version.
Does your shuffle still appear as a USB device in Windows, in Device Manager or elsewhere? If the shuffle has a hardware problem, such as a worn-out headphones jack or bad logic board, the reset utility will not help because the shuffle is not seen by the computer. Also, it's possible that USB docking cable has become faulty (and it's not a problem on the shuffle).
NOTE: The USB cable for the more recent 3rd and 4th (current) gen shuffle does not work with a 2nd gen suffle, because the connector is different.
And be sure rule out a problem with the USB port on the computer by connecting something else to it, preferably something similar, such as a USB flash drive.
If you need to use the reset utility, and know someone with a Mac, Mac OS X can run both 32 and 64-bit apps, so you can run the utility on a Mac. shuffles are always formatted using the Windows disk format (FAT), so you will be able to use the shuffle on your Windows PC after it is "reset" (or restored) on a Mac. If there is an Apple Store nearby, you can make a reservation at the store's Genius Bar and take it there.