Wellllllll, you need a couple of specialized tools that just about every saltwater fisherman has and every freshwater fisherman ought to have.
The little Berkley crimpers shown above will grasp tiny objects tighter than anything you can imagine because the fulcrum (hinge pin in this case) is so close to the end of the jaw (work arm) and the handles (effort arm) are pretty darn long. This gives you a 10:1 mechanical advantage which comes in mighty handy. I use the crimper to grasp the coiled wire portion of the swivel as shown above.
Next, you will need strong split ring pliers, not the mickey mouse type used to handle tiny split rings. (shown below) I don't have anybody handy to help me with the photography at the moment so I will have to try to 'splain it.
Titanium brand Split ring Pliers. Pretty good. About $15.
Grasp the twisted part of one end of the swivel (with crimper) close to the loop as possible. You don't need to hold it terribly tight (remember the 10:1 mechanical advantage you have)with the crimper.) Next, take the split ring pliers and hook the tip over the end of the twisted wire right at the swivel and carefully unwrap the twist. Insert the wire through the spinner blade and re twist.
You will probably break 1 out of 3 or 4 wires even when you get good at the operation but, for what you get, I'll take the risk of breaking the wire.