Welcome to the forum!
Hhmm, do you technically need either a "spiro spline" or "B spline" path? If so, I don't think there's any way to change your calligraphy paths to those. I think you'd have to draw them new. (In that case, you would set the options on the control bar of the Pen or Pencil tool, to whichever you need.)
However, just going by your screenshot, you can accomplish the desired result, although it might end up being a lot of work. Have you ever selected a calligraphy line with the Node tool? To change the calligraphy line to a line like you showed, you'd have to edit the nodes. Just grab them with the mouse and drag them.
I'd probably suggest using Path menu > Simply on the calligraphy lines, before you do that. Because the fewer nodes there are, the easier it will be.
In some cases, you might be able to use a path operation (such as Difference or Intersection). It's hard to suggest the best way without seeing an example of your work.