You can say "It will be my honour" in reply to an important request.

It sounds very stilted, a bit like the way we would expect a knight in shining armour to speak to the King in a mediaeval costume drama. "It would be an honour" is much more natural, though not used very often, but that is because it should only.be used on very special occasions: an honour is a big deal.

You could also say: It will/would be a pleasure.

The correct way of saying this is: I would be honoured/honored (the latter is the American spelling).