You can use a lint roller to get most of the fur off the back also. Just be prepared to change the sticky surfaces fairly often. The lint rollers can do magic - get the fuzzies off, repress if necessary, and fold neatly - might want to check with your quilter if she has allergies to cats, though, before sending it to her.
I would avoid washing it if possible - those seams will fray -
and how do I know this?
Because I had to wash some sewn together strips - I basically soaked them in the sink - rinsed them in the sink - and draped them over a drying rack - minimal handling and agitating - and it still frayed a lot.