Just take a laundry soap jug and use the handle off of them, insert the wire through the handle and you have a better handle than the plastic junk that is already on the pail that came with it.
I have never seen a laundry soap jug with something that would seem suitable. But, I will definitely keep an eye out for them! Thanks for your suggestion. I don't have a lots of the window parts that worked well for this particular bucket.