I use a grill scraper brush thingy too. Wire bristles on one side and scraper on back. I love it!!! I follow it with a stiff bristled (think its boar hair) horse body brush...we had to sell the horses but alot of the grooming stuff is being repurposed....The best tool I found for cleaning cages is a grill brush/scraper. One came with my grill set, but something broke off it...so it became my rabbit cage cleaner...the angle is perfect for reaching the back. But it is too stiff to get down between the wires so I follow up with a stiff nylon brush from the dollar store. I tried the putty knife, works well for the top...but the grill scraper works better because of the angle to it and the long handle.
Duct tape will also bring hair off cages...make a lint roller out of it by pulling a hank of tape off and wrapping it backward (sticky side out) back around the roll or around your hand...it pulls all the loose angora fluff off the walls and corners of my cages without alot of work for me. We use it about once a week.