Elijah is a man of God and therefore the spirit of the Lord would have empowered him with the courage to stand before KIng Ahab.
If he had gone in his own might and strength then he would have had reason to be fearful.
He was in danger because considering he appeared to be an ordinary man, making a declaration that there would be no rain nor dew would have surprised and even angered the King. Elijah spoke against their god (Baal) who they believed to be the god of fertility. To say as Elijah did "at my word" denotes that he spoke with authority, and was certain that that what he foretold would have happened. The King might have thought he was been disrespectful, so his life would have been in danger to approach the king in that manner.
When you are directed by God and anointed to speak "thus saith the Lord", then the fear of men regardless of their status is secondary. So Elijah delivered his message and moved on, no debate, no argument. As powerful and corrupt as Ahab was he had to hear what the man of God said. He did not have to agree but he must be made to understand like our government and other leaders in the world that God is all powerful and all other powers must be subjected to him. As in the days of Eijah God will continue to speak through his true servants. Who can stand against the Lord no one can, no one will.
