Thanks everyone for the comments and suggestions.
In answer to one question, this is "unquilting", not simply "unsewing".
Neither of them are a joy.
I have a box knife blade, so I will try Peckish's suggestion first. I may "sneak" and "borrow" hubby's mustache trimmer too, just to "test" if it works. Come to think of it, I think the horse trimmers are out in the barn... may have to "test" those out as well, and see what happens.
Again, thank you all for your suggestions.