I tried but this method isn't working. Can't find more option there to put signed message. If you have blockchain wallet can you check it please.
You could try following the method mentioned by hosseinimr93. It seems to be the only way around as even I have already experienced the a similar issue before with blockchain.com.
You just need to set a pass phrase to your blockchain wallet and put your passphrase here
https://iancoleman.io/bip39/ to extract private keys to all the address linked to your wallet. And you can even easily sign a message with the help of your private keys online, but I would recommend going with the Electrum method for privacy.