Remember that the early colonists were the working POOR, and they could not afford to spend money on hand weapons. They bought Tools, they could use to build homes, corrals, pens, barns, sheds, etc. out of a wilderness. If an axe ever was used as a weapon, it was in a life or death struggle and only if he could not reach his gun, or it had already been emptied, and he didn't have time to reload it.
The American Indian's use of the hawk was based on a different approach to warfare, and spiritual concerns with taking the spirit, or soul of the enemy you attacked. It was better understood in the Western Plaines, when White trappers and explorers discovered that killing an enemy for some tribes was not as important as touching an enemy with a " coup " stick. The long handled, small edged tomahawks, shown in "The Last of the Mohigans" movie, were used by the Eastern Tribe. But, they were also highly decorated with paint to represent the spirit of the warrior, and his clan, and warfare was a religious event, much more so than it was for Europeans. Indians armed with war clubs- like the Ball-end clubs in fashion these days-- were considered equally well armed as another Indian with a Tomahawk.