most bankers will still ask for screenshots of transactions from your email or exchange in those dates, not signing. I say this from exchange requests asking to show where it came from.
I'd tell them screenshots can be faked, and prove nothing. Instead, I'd send them a signed message, printed on paper for their inconvenience.
LoyceV, you are an experienced bitcointalk member. What was the oldest signature you've seen?
My oldest transaction is from 7.5 years ago. And I'm not going to dig up old backups of Android Bitcoin Wallet (Schildbach) to find the exact transaction.