Damn, that will take a while! 6 years to sync bitcoin wallet, lolwat. Why the hell its became so big? Anything faster?
You don't need to synchronize Bitcoin Core to sign a message AFAIK.
Oh wait, its 14 hours. Ok. Still a lot. Anyway if theres no other way
You could probably import the private key to Electrum and sign there, but that isn't necessary since it should work right away.