Ok, let's get some things clear.
FedEx is a "Common carrier" and thus, not the Post Office. Hand guns cannot be shipped via the Post office, except by FFL.
So, the FedEx return ticket is ok to ship to Charter Arms.
Whatever CA does, when they are finished (barring some obscure VA law) they will ship the repaired gun right back to the return address you provided when you shipped the gun.
Should those repairs require a new serialized frame, CA handles that. They report that Frame number nnnnn is destroyed during repair, and that number yyyyy replaces it. Or they will simply take an unserialized frame from the factory and use that, giving it the s/n of the destroyed frame--even easier for less paperwork.
Now, I don't know a lot about Virginia, what I do know has to do with which bars to not go into in the Little Creek/ Dam Neck areas, and that I have a 300 unit apartment complex building in Chesapeake. However, from what little I do understand, no one in Va LE has the s/n of your Charter Arms, nor much cares, since you are a law abiding Virginian.
Charter Arms does business in California and New York, I'll guess that they can handle Virginia. They sent you the fedex label. I'd put the CA in a boxk, apply the label and let CA handle it the way they handle all their warranty work. This is probably not their first rodeo.