The thought of making your own activated charcoal to filter your Sake is a great idea, but make sure you have the right kind of wood, it can't be treated with any type of chemical.
The act of creating activated charcoal is by super-heating contained wood, coconut shell, or bamboo in a container without the flame of a fire hitting it. As it releases the gases and removes the excess carbon it creates pores. These pores are what will filter your fluids. The more pores the better the filtration.
"Activated charcoal will not filter bacteria, ammonia, nitrates, nitrites, fluoride, sodium and most other cations, significant amounts of heavy metals, iron, copper, hydrocarbons, or petroleum products."
True activated charcoal is only made if you can get fire that burns hotter than normal such as kilns, or furnaces that can reach around 1,800 degrees Fahrenheit. If you are Using a lower heat you will only get a low version of what you intended to get.
There is lots to learn before doing this, such as do you have a membrane that will filter the charcoal mix you make when pouring your sake into it? Membranes are important because they will take out the charcoal "Dust" and turn your black sake into clear sake.
It's cheaper to stick with purchasing the activated charcoal via Amazon, or some other place only after doing research on it. You need to make sure it is food grade though. Food grade is different than normal because they will make sure that there is no other chemical left on the activated charcoal, or even if they used any to start with.