Rear Admiral: The end is inevitable, Maverick. Your kind is headed for extinction.
Maverick: Maybe so, sir. But not today.
Bradley 'Rooster' Bradshaw: My dad believed in you. I'm not going to make the same mistake.
Amelia: Captain, still?
Maverick: Highly decorated Captain.
Maverick: He would always resent me for what I did. Why should he resent her too?
Maverick: You think up there, you're dead, believe me.
Answer: You're correct - when you see Hangman's loadout before he lands back on the deck - he still has all weapons on the rails - it should be that he is short an AIM-9 or an AIM-120 AMRAAM depending on what was fired.
In all shots of Hangman's F/A-18E after the final battle (especially in the close-up right before he lands on the carrier), it is shown that there is an AIM-120 loaded onto the right air intake weapon station. The left air intake station is empty - indicating either no weapon was loaded or an AIM-7/AIM-120 was fired.
You can see that all his missiles are still intact and even if one is missing it would be very unlike to only load on the right and not the left as well. But where he says "This is your savior speaking" you can see all missiles are still on the plane and unfired.