InDesign does not have a wavy line style like Illustrator so you either have to draw it with the Pen or Pencil tool or draw it in Illustrator and Place as a graphic or copy and paste to get an editable line in InDesign.
No, you're mostly right in that ID doesn't have a 'configurable' wavy line, just the one fixed-mode one. I haven't found it very useful, not up against what some other apps have. Then again, there's not much use for wavy lines. 🙂
With the line tool selected and the Stroke palette open, select the wavy line type from the drop-down list.
I believe the same strokes types are available everywhere else a line is defined (frames, borders, tables, etc.) You can scale the thickness of the line and the "waviness" proportionally, but there is not much other control of the wave size and spacing. You can define custom line types, but only using straight lines (although they can be dotted or dashed).