As we often find with Inkscape, there is more than one way to do something. So here's how I would do it.
1 -- Path menu > Break apart. Yes, the whole thing will turn black at this point, but read on.
2 -- Add a stroke (Object menu > Fill and Stroke > Stroke Paint tab, and click the solid color button, which looks like this

)
3 -- Remove the fill (Object menu > Fill and Stroke > Fill tab, and click the big X button, which looks like this

)
Now, what you see are all the paths. You'll have to recombine and re-fill some of the individual paths with black, which were black before. And delete other paths, if I understand correctly what you want to do. And if you want individual words to be a separate object, you'll need to either group them back together, or use Path menu > Combine.