https://ddocompendium.com/w/Headman%27s_Chop
To confirm, there's no benefit if the axe is in the off-hand and a non-axe is in the main-hand, right?
Also, if I have a Battle Axe in my main-hand and a Long Sword in my offhand, will the off-hand Long sword also get the +1 Crit damage on 19-20?