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.