What Bill is stating is that if you study the period techniques then you should be able to quite easily apply them to a weapon such as an axe. There are differences, yes, especially in handling. But the movements and techniques themselves are no huge wall.
Personally I favor a warhammer for my one-handed helm-smasher, but I could see some similar stuff with an axe.
And Sir Wulf, the odds are at your fightclub, few of the members were applying period medieval techniques.