On the Favorites I have seen, they appear to be held in place with metal pins. I would assume they could be backed out (carefully) with a center punch or dull nail to the point they could be grasped by pliers and eased out.
If you don't want to risk damage, an alternative would be to hang the paddles so that everything up to the handles is submerged, and then deal with the remainder with vinegar and wire brush. Wrap the handles with masking tape while you do that.
If you don't remove the handles, you'll have to bake your seasoning on over a stove burner instead of the oven. Hopefully, you'll be able to just get them off without too much trouble.