Here is my feedback/review on the Melee weapons in CKZ2. Do not expect a review on the infamous baseball. There is nothing useful for me to say about the weapon.
Most Powered Up Weapon: Chainsaw
Recommended: Black Katana
Ancient katana - The best melee weapon unless you have enough to buy the chainsaw. It is the same as swing speed of the black katana but only twice its power. If you are willing to get the daily bonus 15 times consecutively then you will be able to get the black katana
Black Katana - Get this weapon when you avail of the daily mission bonuses for 15 consecutive days. You need to be connected to wifi when you complete the daily mission to get the bonus. The survival mission is counted. It has a killing power of 80 and has a fast swing rate. It is no different from the Ancient katana. Only difference is the power.
Fireman's Axe - If you don't have the katanas this is a good replacement for the bat. For 40 glu gold, not bad. Higher damage but not that fast when swinging (compared to the katanas).
Chainsaw - the melee weapon with the highest destructive damage. Reminiscing Ash from the Army of Darkness movie and the Texas Chainsaw massacre films. See those zombies reduced to a pulp with this weapon. At 1100, there is no other melee weapon that compares to this. Also, it does not seem to run out of gas - which is good when you are out of ammo. But that would be a rare case, since with weapons that you buy with gold (300 range) have enough ammo to last you until the next ammo refill. Just having the .30 Lightmachine gun, Annihilator and Streetsweeper is enough for you to finish a regular mission.
Unlike the katanas, the Chainsaw has one flaw - the weapon does not allow it to be swung quickly side to side like a sword. Normally, you just have it running in front and stick it at the zombie. You swing left to right and zombies go bye bye. Only the stronger zombies like the security guards get a slim chance of damaging you before they die. Is this a good weapon? Yes, as long as you don't use it against a Bomber or Spitter (unless you are suicidal). I haven't tried it against a Smasher powered up with a damage boost.
The Wolf Pack are my friends, like all others whom I have the pleasure to know. You have my respect because you deserve it - the same way I expect this respect from you as well.