I am not sure how the fuse would work, you would have to use a synthetic setting on your iron, and I don't know if it would be hot enough to fuse the cotton fabric.
I would definitely use a walking foot for stitching on this, and I would be more tempted to use cotton fabric for the binding... Maybe wash and dry the flannel a couple of times, as the fur isn't going to shrink at all, and the flannel can shrink through several washings...