Yizhi will point out that the Shuten's food/water supply can't be easily tampered with from their current position, and their Lost Souls will probably be on guard against Tamamo reps trying to sneak them laced food. But it's a very good idea otherwise!

Perhaps some of them could infiltrate Shuten territory to see if poisoning is possible + start talking to the civilians. If they can find a way to get into Shuten food or drink without getting caught, the poisoning idea becomes 100% feasible.