I already tried everything possible. I googled regarding the same and even I checked on this forum as well but yet can't find the exact solution to sign a message from blockchain wallet.
that should help you, shouldn't it?
already tried to import the address (you have seed, right?) into electrum and sign it there?
You cannot sign message directly on their site, at least for now. But, if you have backup seeds, just import it to electrum and sign message from there or you can use
BIP39 Iancoleman(use it offline) and write your seeds on there and just search your address, import the private key from address that you want to sign to your blockchain wallet via imported address and you will able to sign message from there.
I have never changed my email address on my profile and still I am actively using the email mentioned on my profile.
that might be helpful.