If by "charger," you mean the part (a power adapter) that plugs into the wall outlet (NOT the cable), it should work fine with your iPod nano's USB docking cable. iPod shuffles did not come with any power adapter, so I'm not sure what an "iPod shuffle charger" is.
Do NOT plug an iPod shuffle USB cable into the iPod nano's headphone jack. The iPod nano charges (and syncs) through the dock connector, not the headphone jack.
If you friend has something like this
you can plug your USB docking cable into it and charge your iPod nano. But to repeat, do NOT use the shuffle's USB cable with an iPod nano.