I don't know those circuits offhand, but I'd be surprised if the voltage gauge and cig lighter are on the same circuit and fuse. But it's possible. You'll want to look at the ESM. Those lighters commonly have a fusible link built-in. If there is one, it could have burned up if there was a short in the charger. Is there still power there? Maybe it's just a coincidence that something happened to the dash with the charger in. What makes you think there is a connection?
Anyway, I would get the ESM, look it up, and start checking fuses and circuits in a methodical way. But if everything else works fine, it's not like you can't be without that voltmeter for a bit.