I agree with all the other 1h axes being terrible, that's why i don't use them. So i could see some buffs for the Iron War Axe and One Handed Battle Axe(non-broad). They are inferior in most ways to the 1h Broad Axe;
Iron Axe- 3 points less of speed, 4 less reach and higher difficulty for only 2 more cut damage. I think it could use a damage buff to compensate for the low speed and reach.
One Handed Battle Axe- 1 less cut and 1 more str point required for 3 more reach. This could use maybe some more reach but with less speed or damage, as to not make the Broad Axe inferior.
I quickly thought of the balancing stuff so please put some input on these suggestions.