You'll probably have to duplicate everything and delete the parts you don't need...
On this occasion, I realized that "inverting" the selection won't select nodes on other, non-joined segments, so you'll have to select them the hard way.
I see what you mean though. Right now, if you have a combined path and select+copy one part, pasting would paste the whole combined path rather than that one section.
I guess the issue here is that nodes aren't free-floating objects to copy/paste, so if you copy/paste non-continuous nodes then it wouldn't make sense.
It could be an interesting feature though: - If you select several nodes on a continuous path and copy/paste them, you get a new continuous path with those same nodes (but without the uncopied nodes) and the same handle values (?) as those nodes. - The process repeats for all segments of paths selected - If for one continuous path, only a single node is selected, then nothing happens.
It could be called "paste segment" or the likes.