Method 1
What you need for this fix are two rondelle beads and a length of a hat pin blank. For each rivet you need to fix. It’s important that the head of the pin be large enough not to slip thru the hole in the bead.
You need to thread the pin thru one rondelle bead and thru the pivot holes and thru another bead. Cut the extra pin length off with about 3/8″ extra.
Use some jewlery pliers to loop the extra wire back to the hole area. You can use this for your twist cord for your tassel set. My tassel articles.
This is what it looks like from the head side of the hat pin.
Method 2
To do a proper rivet you need a brass Escutcheon pin and a washer. Here I have a special washer which has a fold over (something like a clamshell used in jewlery making). I only have a few of these I have scavenge. But this can be done with a small brass washer. Also, if you can find soft silver metal pins and washers you might be able to do it as well.
I first thread all the ribs and guards onto the pin in order and use tape to hold the pin in place on one side but hang over on the other.
You will need an anvil or hard metal surface to prop the pin over. This is where it might be nice to have a helper hole the fan.
I found it difficult to hole it and pound so I used some more tape to hold the fan in place.
Using a hard metal tool like a screwdriver with a blade wider that the guard hold it as close to the edge of the guard as you can. Make sure the head is taller and pound it with a hammer to make a dent the round pin.
I switched to a drill bit (for a 5/8″ hole) because it stuck up higher and I could pound on it and not risk hitting the fan.
Cut the pin leaving the full width of the flattened part ~1/8″.
First pad your anvil, then set the fan vertical. With a hammer pound on the flattened part of the pin until to rolls over or spreads out so much that it can not slip thru the hole of your washer.
While you are hammering on the pin end it very easy to bend the rest of the pin so it’s important to keep you fingers tight on the edges of the fan to keep this from happening. Now I can fold the solid part of my washer over to cover the rolled edge of the pin.