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.
I actually suggested this method once, but there were 2 problems. Firstly, the customer support didn't understand what this was lol and that made it all useless. Secondly, I admit I didn't know how to sign a message from my other non BTC wallets. MetaMask for Ethereum didn't have this option, not to mention dogecoin and others I kept on multicrypto wallets (yes I know I'm dumb with shitcoins).
Many people dont even understand bitcoin, how would they trust a signed message. This is something very bitcoin specific and is not possible with a normal bank account or anything else. I think we need 20 more years for stuff like this.