Removing Wire Rust Stains from White Lampshade

[weft2]

I have a very nice curved white lampshade, but parts of the wire frame
behind it have rusted and also rust stained parts of the silky looking
material on the outside of the white lampshade. Not sure if the shade
material is cotton or polyester, but is it possible to remove the
stains, or will it just make the problem worse, since anything wet
applied to the shade will also wet the source of the rust- the wire
frame. Also, won't the stains just come back later, even if they can
be removed? I wonder why the makers of these lampshades don't coat the
wire frame with a light epoxy paint. I've seen many discarded and
lovely lampshades that were in good physical form, except for rust
stains along the wire framework.

Thanks for any info offered