I have a multi-tiered sewing box that has articulating wooden arms on the outside (the tiers slide out similar to some tackle boxes). I recently re-finished the wood but when I took it apart I noticed these thin felt or paper pads between the sides of the box (at the screw holes) and the arms which I believe were to help with friction and prevent the sides of the boxes from being scratched when opening/closing. Does anyone have ideas of what I could do to replace these? Perhaps just a simple round sticker, or a small piece of felt, or those hole protectors for 3-ring binder pages?
You can use the plastic from many common food packages to make little washers for this purpose.
I've used the softer plastic from the flexible lids to a few food canisters, e.g. Cadbury's cocoa, in the past which is polyethylene (PE, recycling symbol 4):
The high-density version HDPE (recycling symbol 2) as used in plastic milk bottles can also be used. I think you can also make suitable washer from polypropylene (PP, recycling symbol 5).
These plastic washers can actually work better than the felt ones originally fitted to the box, giving an excellent service life. If they ever do wear out they're very cheap to replace :-)
The challenge is actually making them since it's not obvious the best way to go about it. It is very easy to distort or split small pieces of plastic if you make the discs first and then try to drill holes at their centres. So drill the holes first spaced around a larger piece and then cut or punch the circles around each hole.
You can cut the outside shape just with scissors if you had to, they don't have to be perfectly circular to function, but a leather punch can do an excellent job if you happen to have any and they will give a very neat finish. Note that the holes don't have to be dead in the centre for the washer to work well so if you're a little off don't sweat it.
You can also get neat circles, with perfectly central holes, by cutting the plastic roughly to shape and then mounting them on a mandrel which you then chuck up in a low-speed drill. You then run the edges against sandpaper or a file as the drill spins. If you want to slightly polish the edges you can run the drill faster and gently rub with a piece of fabric such as a scrap of denim.