Problem

I would like to make axes still have the new pvp mechanics

Proposed solution

Add an option in the config for both weapons

Example:
disable-attack-cooldown:
This is to disable the attack cooldown
enabled: true
worlds: []
What to set the attack speed to. Default for 1.9 is 4, at least 16 is needed for no cooldown.
generic-attack-speed: 24
adds an exception to this rule
axe-exception-enabled: true
sword-exception-enabled: false

This is not possible because the cooldown is a player attribute, and not a per-tool attribute.