I have about three different 13/64 diameter Oscar rivets that Fleetwood used in the era of our rig. Personally I use 1/16 Molly's which are for number 6 screws. If you have to stay with very short item for a permanent fix use a threaded rivet. You do need a tool for inserting them and replace the wood screws with threaded screws.
The threaded rivets or inserts can be installed with a long screw and nut like a jack nut. Jack nuts are basically like a molly but no screw included and have a much bigger shoulder than an threaded insert. I have installed all three items with similar tools. The molly usually requires a screw driver while a pop rivet and blind or threaded insert use a tool that is very similar.
If you look them up and read the literature about each one you'll end up wanting all of them around for repairing things.