Humans have cores. They have more cores than undead do. One stab through the brain and they're gone. One stab through the heart and they'll be dead in seconds. One stab through the throat or two stabs through the lungs and they'll quietly die in a short while. Perhaps we should stop this ultra specific testing before it gets ridiculous.
Get some clothes, enough to make Piecewise look like a human. Also try to make it thick to provide defense against blunt force trauma, unless doing so would significantly hinder his speed. Finally, ask Bruce to borrow a pan or some spare piece of metal and tie it around Piecewise's core and something long and sharp that can be used as a rapier. (Maybe some sort of sharp pick he uses for sculpting details?) Hopefully they should be enough to help bypass any armor, but I'm guessing a lovely patrol won't be armored like a SWAT unit so they'll have at least some unarmored parts.
The second part of the plan is to get Esme to grant us knowledge from one of her books (probably a medical or swordfighting one) with the goal of learning the human body's weak points. It won't make us an expert fighter but it should hopefully let us better direct Piecewise's attacks, which should be our primary objective. That way he can kill more quickly, more quietly and have more options about bypassing armor.
Finally, ask Esme what would warrant a response from a patrol. An anonymous tip about suspicious activity? Anti-government graffiti? Calling them and taunting them? We want our enemies to be weak and few, so we can't do something very serious. But we would also like to not involve innocent cops that are just doing their job, so we might want to do something that would involve the military. Unless doing so would be very hard or there's no meaningful distinction between cops and military.
With all that done, we can find an abandoned location and start planning our attack. Maybe there's an empty lot or abandoned construction site or factory around here?