Looking at the user manual online, it shows that you can connect the USB and the AC to the Cradle.

You may find that you have a second hole in the cradle that will take the AC.
Usually it is a round hole, you may have to remove the flat end from the AC cable.
Or perhaps the cable you have is only for connecting directly to the PPC, if that is the case maybe you need to buy a different cradle or cable.
Another possibility is to sync via Bluetooth while you are connected to the AC, not sure if that would work for an update, or even if you have BT.