No other comic book character suffers greater from revamping than Hawkman. He has one origin from the Golden Age, a new one from the Silver Age, and one from the modern age that is a mish-mash of both. Even as well written I believe the latter is, penned by Geoff Johns, Hawkman still comes off as misdirected. The resolution using the best of all the conflicting tales is as follows;
The Golden Age
In ancient Egypt there was Prince Khufu, powerful and benevolent. Along with his bride Shiera they ruled their lands in peace. One day they come across the wreckage of a crashed Thanagarian spaceship. Inside are the bodies of two explorers and a cache of strange metal that seems to call to them. Khufu has some of the metal taken and orders the ship buried, fearing one of the Egyptian gods might discover it and be angry for Khufu's interference.
The metal is Thanagarian "Nth Metal," Khufu and Shiera discover wearing it gives them increased power and the ability to fly. They fashion tunics made from it and use it to help seal their rule. Jealous of their new power, the all-mighty Teth Adam, champion of the wizard Shazam kills them. This is the crime Adam commits to lose his place as Shazam's champion, he is stripped of the word and cast to earth devoid of his memory sentenced to walk the planet an immortal beggar.
Fast forward to 1940's America. Museum curator and archeologist Carter Hall learns he and his wife Shiera are the reincarnated forms of the Egyptian rulers. The strange Nth Metal apparently has mystical qualities and after being exposed to it for so long, has intertwined itself with the very souls of Khufu and Shiera. As archeologists Carter and Shiera also discover the mysterious "ninth metal" which increases their strength and allows them to fly. The couple decide to join the ranks of other 1940’s mystery men and become Hawkman and Hawkgirl, using ancient weapons from their museum to fight crime.
Their adventures unfold as written at the time.
The Silver Age
Alien police officers Kator and Shiera Holl, of the distant planet Thanagar, come to earth to study police methods and fight crime. This is the first attempt to reach earth since the failed maiden voyage centuries ago. Being that the police force on Thanagar also wear the signature hawk uniforms, they become the new Hawkman and Hawkgirl. The two have their silver age adventures and stay on earth until their natural deaths years later.
The Modern Age
Fast forward to today. Once again Khufu and Shiera are reincarnated but this time Carter has memories of the past lives. He discovers the remains of the Thanagarian Hawkman and Hawkgirl from the Silver Age, and helps fill in the gaps to his love Shiera. Now they use both futuristic Thanagarian weapons and ancient earth maces and spears in their fight against evil.
Now we have two sets of Hawkmen and Hawkwomen but both golden and silver age elements remain. I believe this set up uses the best of the conflicting origins, you just have to allow for the Silver Age alien invention. You give the miracle Nth Metal a supernatural ability, which affects both Earth and Thanagarian couples across time and space. Of course this will never happen but, ah well.