Help with custom charging dock for prop I'm making

[warmachine2]

First off I dont have much experience with electrical work, but I'd like to really get into it.
I want to buy or build a battery and charging dock for this light up prop kn making. It's basically like a flashlight. It's about an inch diameter cylinder and I'd like it to be able to dock into a charging stand like a walkie talkie charger.
I cant seem to find the right terms to buy it or to find how to make one. Can anyone tell me how they work or where I could buy something close? Perhaps what that type of charger is called?

 

[GoldDigger]

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