The Puritan is a Favorite made WI, and those rivets holding the handles in place are peened, and very difficult to remove without damaging the iron. When cleaning Favorite Waffle Irons I do not attempt to remove the wooden handles. I know one person who has removed them, but I just did not want to risk damage.
So, I rigged a special lye bath, and sleeved the wood handles using nitrile gloves , and filled the lye bath to just cover the Cast Iron, and not touch the wooden handles....
Then I customized the hangers to hang them in the Electro, once again sleeving the wooden handles to protect from Moisture.
The Good Health paddles, I believe they will screw off, however I have not done any paddles with those style coils, so maybe someone else can chime in also.... Removing coil handles usually requires treating the area with Liquid Wrench, Seafoam Deep Creep, or Kroil.