If anything the Pipe Baton should get a buff. It's equivalent to all the other starting melee weapons, but instead of being crafted from basic stone age materials it requires glue and pipes.
A better fix though would probably be to make the wood club benefit from either Pummel Pete, or Electrocutioner, whichever is higher. Then move the Pipe Baton up to being the Tier 2 weapon, and then bump the Stun Baton to Tier 3.
I think what I'd really like though would be unbinding the melee weapons from the different attributes. Then change the melee skills to give generic bonuses to all melee weapons. So you'd have one for raw damage %, another for knockdown, another for stun, another for dismember, another for attack speed