if your stove isn't too big the sticks you use should not be too long, what I would do is get a decently deep aluminum bucket/trash can, and when you want to "put out the fire" just grab the sticks and pull them out while they are on fire and have some water in the bottom of your aluminum pail, if the flame isn't too big when you pull the sticks out you can almost blow it out (not always) but if you were to either "dip" the burnt parts in it would immediately extinguish the fire, or you could just drop them in said pail without water (pail should be outside when you do so) and just let the wood sputter out or burn out inside that pail (obv pail shouldn't be expensive)
