Put the stick in the characters hand.
then pose the fingers to grip it.
Go to your rigs object data tab and create a new pose library. it is closer to the bottom of the tab.
when you click new you will get a new window that pops up right under it.
select the finger and wrist bones then press the plus button on the right and call it closed fist or something.
Note that if you want to re apply this pose just select the bones again and click the orange magnifying glass thing at the bottom right
then select your stick and go to the object constraints tab
and give it a child of constraint
Select the target as your character's rig and the bone as it's wrist
then make sure to click the set inverse button or you will get some weird effects. And if you want the guy to drop the stick just slide the influence slide down to zero.