You might be able to wash it on a handwash cycle or some kind of gentil cycle if you sew all the way around the quits edge at about 1/4" as if you were sewing on another border but use no fabric. Does that make sense? I had to do this with a quilt that was to be sent to the quilters, but the quilt didn't have borders on it. I didn't want it to fray so I sewed around the edges.
Then dry in the dryer on no heat setting.
I am not goign to guaratee that will work, but it did for me. If it were me, I would do it, but that's just because I don't have the time to use a lint brush on a quilt for that long. I'm lucky I have time to get a quilt done ever...lol
Lynette