Pete fights with a walking stick (I also see Alex using the same stick during certain scenes). It is difficult to see, but here is a photo from the scene where Alex beats on his droogies:
This is likely a custom Irish walking stick. I found a good, cheap, durable walking stick that looks similar - the Irish blackthorn walking stick. It is around $50-$100 for a one, depending on the material used. The knob is a tiny bit off and it is a bit darker in shade, but it is very close.