Remove the fill, if there’s one, let the black outline stroke stay. Make a spare copy of your shape, you may need it later.
Select the shape. Goto Path > Stroke to Path. That transforms the outline stroke to filled area.
Use the shape to clip the image. The outline acts as a clipping mask, because it’s now a filled area.
Not asked Scrap the idea of using Clip > Set. Change the stroke color to white and use Object > Mask > Set. Mask is a way to affect transparency with color, white = fully opaque.