which are the best? bladed and firearms are not included. the karate school i used to train at offered okinawan kobudo as well which included bo staff, tonfa, and sai. the tonfa is what the nightstick is based off of so that type of training would b beneficial to LEOs I reckon. I also think there is some merit to stick fighting as you could pretty much utilize those techniques with any cylindrical object I reckon.
Pikiti man pikiti 
If you include bladed weapons you have a lot more to choose from.
stevekt - If you include bladed weapons you have a lot more to choose from.
okay we can discuss them too. but they serve different purposes. not all situations call for katana decapitations which is why i stressed non bladed in the op but for the sake of discussion lets just talk weapons.
most effective melee weapon? id probably say katana
How can anyone not love nunchaku? That's gotta be your go-to if you can't use blades! 
I don't know anything about it but I'd say it's just like other martial arts.
The ones that work involve live sparring, wrestling, Jiu-Jitsu, boxing, Muay Thai, ect.
Find one that soars with blunt weapons and it's going to be closer to the real thing than one that does all kata movements
Fencing kendo larping
And eskrima
I know you said that you don't count edged weapons, but I think the Israeli knife fighting stuff is really pretty bad ass. I also think shooting absolutely qualifies as a martial arts science.